test2.json

[{"text": "this next problem is a bit of a classic", "start": 0.03, "duration": 3.599}, {"text": "and I've actually gotten multiple", "start": 2.52, "duration": 3.239}, {"text": "requests to do some variation of this", "start": 3.629, "duration": 5.161}, {"text": "problem so it says find the volume of", "start": 5.759, "duration": 6.42}, {"text": "the largest open box open box that can", "start": 8.79, "duration": 6.0}, {"text": "be made from a piece of cardboard 24", "start": 12.179, "duration": 5.221}, {"text": "inches square so let me draw my piece of", "start": 14.79, "duration": 5.399}, {"text": "cardboard that's not a llama I don't", "start": 17.4, "duration": 6.6}, {"text": "want to draw it filled in so my piece of", "start": 20.189, "duration": 5.991}, {"text": "cardboard is it's going to be a square", "start": 24.0, "duration": 4.289}, {"text": "I'll draw it pretty big because I want", "start": 26.18, "duration": 4.21}, {"text": "you to visualize it and it's 24 what did", "start": 28.289, "duration": 6.601}, {"text": "they say 24 inches square so it is 24 by", "start": 30.39, "duration": 9.15}, {"text": "24 square by cutting equal squares from", "start": 34.89, "duration": 6.48}, {"text": "the corners and turning up the sides so", "start": 39.54, "duration": 2.85}, {"text": "what are they saying well they're say", "start": 41.37, "duration": 2.43}, {"text": "we're going to cut equal squares from", "start": 42.39, "duration": 4.41}, {"text": "the corner so let's say we cut a and let", "start": 43.8, "duration": 6.3}, {"text": "me see if I can draw this well so I'm", "start": 46.8, "duration": 9.54}, {"text": "going to cut a square here and I'm going", "start": 50.1, "duration": 9.0}, {"text": "to cut an equal size square there I want", "start": 56.34, "duration": 5.43}, {"text": "to draw this neatly and then I cut it", "start": 59.1, "duration": 7.65}, {"text": "equal size square there and then it cut", "start": 61.77, "duration": 10.13}, {"text": "an equal size square there right there", "start": 66.75, "duration": 7.11}, {"text": "so I'm going to cut out those corners", "start": 71.9, "duration": 5.55}, {"text": "and then I'm going to fold up the sides", "start": 73.86, "duration": 6.81}, {"text": "right just so you can visualize it so", "start": 77.45, "duration": 4.69}, {"text": "those dotted lines are where I would", "start": 80.67, "duration": 3.36}, {"text": "actually fold the box and then I would", "start": 82.14, "duration": 3.269}, {"text": "end up with an open box and let's see", "start": 84.03, "duration": 3.42}, {"text": "what the dimensions would be and and", "start": 85.409, "duration": 3.061}, {"text": "that's actually what the whole crux of", "start": 87.45, "duration": 3.69}, {"text": "the problem is so how big of a squares", "start": 88.47, "duration": 5.16}, {"text": "should I cut out in order to maximize", "start": 91.14, "duration": 5.28}, {"text": "the volume of the box well these are", "start": 93.63, "duration": 4.71}, {"text": "equal sided squares that I'm cutting out", "start": 96.42, "duration": 3.989}, {"text": "so let's say that each side is X so if", "start": 98.34, "duration": 5.639}, {"text": "this is X then this is X this is X this", "start": 100.409, "duration": 6.511}, {"text": "is X this is X this is X this is X this", "start": 103.979, "duration": 5.611}, {"text": "is X and then what is going to be the", "start": 106.92, "duration": 4.409}, {"text": "volume of our box that when we when we", "start": 109.59, "duration": 4.05}, {"text": "fold up everything let me see so I'll", "start": 111.329, "duration": 4.801}, {"text": "draw the base so this dotted square", "start": 113.64, "duration": 3.86}, {"text": "right here that's going to be the base", "start": 116.13, "duration": 6.15}, {"text": "right I'll draw it at an angle that's", "start": 117.5, "duration": 6.909}, {"text": "the base and what are the dimensions of", "start": 122.28, "duration": 2.689}, {"text": "the base", "start": 124.409, "duration": 3.781}, {"text": "well this base is going to be the length", "start": 124.969, "duration": 5.65}, {"text": "of this side of the cardboard minus this", "start": 128.19, "duration": 4.31}, {"text": "X minus this X right", "start": 130.619, "duration": 6.171}, {"text": "so this base right here that is going to", "start": 132.5, "duration": 6.9}, {"text": "be 24 minus 2x right it's just the whole", "start": 136.79, "duration": 4.47}, {"text": "length minus this minus that that's how", "start": 139.4, "duration": 3.99}, {"text": "long that is and of course this is going", "start": 141.26, "duration": 3.42}, {"text": "to be the same length this is going to", "start": 143.39, "duration": 3.21}, {"text": "be that same length all of these sides", "start": 144.68, "duration": 5.39}, {"text": "of the base are 24 minus 2x so it's 24", "start": 146.6, "duration": 7.65}, {"text": "minus 2x and then and then this side is", "start": 150.07, "duration": 7.63}, {"text": "also 24 minus 2x and then what is going", "start": 154.25, "duration": 6.6}, {"text": "to be the height of this of this open", "start": 157.7, "duration": 5.13}, {"text": "box that we're creating so let me draw", "start": 160.85, "duration": 8.04}, {"text": "the sides of it it's open which means it", "start": 162.83, "duration": 9.54}, {"text": "doesn't have a top to it right so we", "start": 168.89, "duration": 5.25}, {"text": "have an opening here so you can kind of", "start": 172.37, "duration": 4.77}, {"text": "see the inside of the box and what is", "start": 174.14, "duration": 4.83}, {"text": "this height well when you fold these", "start": 177.14, "duration": 4.47}, {"text": "flaps up when you fold these flaps up", "start": 178.97, "duration": 6.3}, {"text": "the X the height is X right if you can", "start": 181.61, "duration": 4.41}, {"text": "think about it", "start": 185.27, "duration": 2.67}, {"text": "this side here there's really just a bit", "start": 186.02, "duration": 3.24}, {"text": "of visualization this side right here", "start": 187.94, "duration": 3.69}, {"text": "that you can view as this thing right", "start": 189.26, "duration": 4.5}, {"text": "here I can even do it in different color", "start": 191.63, "duration": 4.95}, {"text": "for you you can view this side this", "start": 193.76, "duration": 6.83}, {"text": "front facing side is this right here", "start": 196.58, "duration": 6.18}, {"text": "I'll just do a couple you don't have to", "start": 200.59, "duration": 4.149}, {"text": "do all of the sides I don't think you", "start": 202.76, "duration": 6.69}, {"text": "could view this side is this side right", "start": 204.739, "duration": 7.081}, {"text": "here right it's folded up and then that", "start": 209.45, "duration": 4.59}, {"text": "this back side is this back side and", "start": 211.82, "duration": 3.69}, {"text": "that side there is that and this is the", "start": 214.04, "duration": 4.8}, {"text": "base anyway so that is the volume of our", "start": 215.51, "duration": 5.97}, {"text": "of our open box and we want to maximize", "start": 218.84, "duration": 5.28}, {"text": "it so how do we do that well let's write", "start": 221.48, "duration": 4.56}, {"text": "the volume is a function of X and then", "start": 224.12, "duration": 3.75}, {"text": "take its derivative figure out where the", "start": 226.04, "duration": 3.33}, {"text": "derivative is zero and hope that that's", "start": 227.87, "duration": 2.91}, {"text": "a maximum point and we'll prove it by", "start": 229.37, "duration": 3.36}, {"text": "taking the second derivative seeing now", "start": 230.78, "duration": 3.209}, {"text": "we actually want it to be concave", "start": 232.73, "duration": 2.759}, {"text": "downwards because concave downwards", "start": 233.989, "duration": 3.421}, {"text": "looks like that so that means you found", "start": 235.489, "duration": 4.771}, {"text": "a maximum point so we know that the", "start": 237.41, "duration": 6.18}, {"text": "volume as a function of X I like writing", "start": 240.26, "duration": 5.699}, {"text": "the big v's the volume is a function of", "start": 243.59, "duration": 5.16}, {"text": "X is that side x you know you could view", "start": 245.959, "duration": 5.25}, {"text": "it as depth times length times height so", "start": 248.75, "duration": 7.049}, {"text": "it's X the height times you could the", "start": 251.209, "duration": 10.98}, {"text": "depth 24 minus 2x times the width", "start": 255.799, "duration": 10.33}, {"text": "24 minus 2x now let's see if I can", "start": 262.189, "duration": 5.771}, {"text": "multiply this out it's probably the", "start": 266.129, "duration": 3.961}, {"text": "hardest part about this problem so x", "start": 267.96, "duration": 6.569}, {"text": "times was 24 times 24 it's I want to say", "start": 270.09, "duration": 6.329}, {"text": "it's what is its 4 what I mean I", "start": 274.529, "duration": 4.621}, {"text": "actually it's kind of sad but I've made", "start": 276.419, "duration": 5.4}, {"text": "so many careless mistakes recently that", "start": 279.15, "duration": 4.079}, {"text": "I don't want to make any more and I want", "start": 281.819, "duration": 2.97}, {"text": "to get the right number so 4 times 4 is", "start": 283.229, "duration": 3.111}, {"text": "16", "start": 284.789, "duration": 9.84}, {"text": "4 times 2 is 8 96 0 2 times 24 is 48 6 9", "start": 286.34, "duration": 12.91}, {"text": "Plus 8 is 17 576 that's what I thought", "start": 294.629, "duration": 6.66}, {"text": "it was I should have memorized my times", "start": 299.25, "duration": 4.11}, {"text": "tables up to 25 but anyway 24 times 24", "start": 301.289, "duration": 10.141}, {"text": "is 576 576 and then we'll have 2 times", "start": 303.36, "duration": 9.299}, {"text": "24", "start": 311.43, "duration": 5.88}, {"text": "so that's 48 X but we have them twice so", "start": 312.659, "duration": 8.551}, {"text": "it's minus 96 X right because 2 X times", "start": 317.31, "duration": 6.65}, {"text": "24 minus 2x times 24 then minus 2x times", "start": 321.21, "duration": 6.929}, {"text": "24 so it's 48 2 plus 48 so minus 96 X", "start": 323.96, "duration": 8.109}, {"text": "and then finally the last 2 plus 4x", "start": 328.139, "duration": 7.381}, {"text": "squared 4x squared and now we can", "start": 332.069, "duration": 5.82}, {"text": "multiply the X's out and we get the", "start": 335.52, "duration": 6.509}, {"text": "volume of the open box is let me put the", "start": 337.889, "duration": 7.71}, {"text": "X term first 4x to the third I'm just", "start": 342.029, "duration": 10.31}, {"text": "multiplying this out - 96 x squared plus", "start": 345.599, "duration": 12.09}, {"text": "576 X let me erase this my I should have", "start": 352.339, "duration": 8.371}, {"text": "been able to do that in my head anyway", "start": 357.689, "duration": 6.09}, {"text": "I'm not too proud to show that I didn't", "start": 360.71, "duration": 7.5}, {"text": "know that let's see so let me erase that", "start": 363.779, "duration": 10.26}, {"text": "let me erase that and so what do we want", "start": 368.21, "duration": 7.03}, {"text": "to do we want to take the derivative of", "start": 374.039, "duration": 3.331}, {"text": "this figure out at what value X values", "start": 375.24, "duration": 5.609}, {"text": "do we have a 0 slope and then test to", "start": 377.37, "duration": 4.56}, {"text": "see if those were maximum or minimum", "start": 380.849, "duration": 2.79}, {"text": "points if we have a maximum point at", "start": 381.93, "duration": 3.269}, {"text": "that x value and if it's a global", "start": 383.639, "duration": 3.661}, {"text": "maximum that we have found the x value", "start": 385.199, "duration": 4.921}, {"text": "that optimizes the Vout the volume you", "start": 387.3, "duration": 4.32}, {"text": "might want to graph these and experiment", "start": 390.12, "duration": 2.579}, {"text": "with them and get them more into", "start": 391.62, "duration": 2.669}, {"text": "intuitive sense of it but that's really", "start": 392.699, "duration": 2.761}, {"text": "what we did and when we", "start": 394.289, "duration": 3.121}, {"text": "found minima and Maxima and we did", "start": 395.46, "duration": 3.81}, {"text": "concave upwards and downwards and all of", "start": 397.41, "duration": 6.84}, {"text": "that so anyway what's derivative V prime", "start": 399.27, "duration": 11.579}, {"text": "of X is equal to 12x squared this parts", "start": 404.25, "duration": 10.139}, {"text": "the fun part 12x squared minus was it", "start": 410.849, "duration": 14.491}, {"text": "180 192 192 X plus 576 plus 5 that says", "start": 414.389, "duration": 13.65}, {"text": "576 and it's hard to read talk to read", "start": 425.34, "duration": 4.47}, {"text": "for me so let's figure out where this", "start": 428.039, "duration": 4.141}, {"text": "equals 0 so we want to know where 12x", "start": 429.81, "duration": 10.859}, {"text": "squared 12x squared minus 192 X plus 576", "start": 432.18, "duration": 12.66}, {"text": "is equal to 0 and the easiest thing to", "start": 440.669, "duration": 5.37}, {"text": "do here is just to divide the whole", "start": 444.84, "duration": 2.85}, {"text": "thing by 12 both sides because when you", "start": 446.039, "duration": 3.271}, {"text": "divide 0 by 12 you still get 0 so you", "start": 447.69, "duration": 4.009}, {"text": "get x squared", "start": 449.31, "duration": 5.37}, {"text": "- what's 192 divided by 12", "start": 451.699, "duration": 8.681}, {"text": "well 192 was 24 times 4 right it was 20", "start": 454.68, "duration": 12.359}, {"text": "to 24 times 4 is what is is that right", "start": 460.38, "duration": 10.71}, {"text": "24 no no 24 times oh I just go to 24", "start": 467.039, "duration": 9.361}, {"text": "times 16 is 192 right actually I just", "start": 471.09, "duration": 6.66}, {"text": "want to be I've been making so many", "start": 476.4, "duration": 4.16}, {"text": "careless mistakes 12 wasn't when I do", "start": 477.75, "duration": 6.24}, {"text": "112 72 or at 16 I should have been able", "start": 480.56, "duration": 8.169}, {"text": "to anyway - 16 X plus well this was 24", "start": 483.99, "duration": 8.31}, {"text": "times 24 so this is also you could this", "start": 488.729, "duration": 5.91}, {"text": "would be 12 times 48 so this should be", "start": 492.3, "duration": 7.44}, {"text": "plus 48 is equal to 0 and we could write", "start": 494.639, "duration": 9.571}, {"text": "24 times 24 is 5 plus 76 so 12 times 48", "start": 499.74, "duration": 6.66}, {"text": "right so now we just have to factor this", "start": 504.21, "duration": 6.209}, {"text": "so what two numbers that when I add them", "start": 506.4, "duration": 8.55}, {"text": "I get minus 16 and then when I multiply", "start": 510.419, "duration": 9.3}, {"text": "them I get 48 positive 48 let's see 6", "start": 514.95, "duration": 7.709}, {"text": "times 6 times let me make sure I did", "start": 519.719, "duration": 6.631}, {"text": "this so 12 12 goes into 72 6 times", "start": 522.659, "duration": 5.251}, {"text": "let me I just want to make sure I have", "start": 526.35, "duration": 2.76}, {"text": "the numbers right as you can tell I", "start": 527.91, "duration": 2.43}, {"text": "don't do these problems ahead of time", "start": 529.11, "duration": 2.64}, {"text": "because I want you to see that I go", "start": 530.34, "duration": 3.21}, {"text": "through the pain as you do so let me", "start": 531.75, "duration": 6.03}, {"text": "make sure I 12 goes into 576 12 goes", "start": 533.55, "duration": 11.01}, {"text": "into 576 what five four times 48 48 and", "start": 537.78, "duration": 11.67}, {"text": "you get 96 12 goes into 90 right 48", "start": 544.56, "duration": 6.99}, {"text": "times 12 goes I shouldn't have had to do", "start": 549.45, "duration": 3.99}, {"text": "that but I've been making so many", "start": 551.55, "duration": 2.82}, {"text": "careless mistakes", "start": 553.44, "duration": 2.88}, {"text": "I haven't eaten dinner yet so anyway", "start": 554.37, "duration": 4.38}, {"text": "maybe I'm just missing the easy factor", "start": 556.32, "duration": 4.56}, {"text": "right because I have what numbers you", "start": 558.75, "duration": 3.99}, {"text": "get 12 times Oh actually I just figured", "start": 560.88, "duration": 5.85}, {"text": "it out twelve times four sometimes when", "start": 562.74, "duration": 5.19}, {"text": "your brain is in calculus mode the", "start": 566.73, "duration": 3.27}, {"text": "algebra 2 gets difficult so this is the", "start": 567.93, "duration": 7.62}, {"text": "same thing as X minus 4 times X minus 12", "start": 570.0, "duration": 11.79}, {"text": "is equal to 0 so at X is equal to 4", "start": 575.55, "duration": 8.64}, {"text": "we're at some type of minima or Maxima", "start": 581.79, "duration": 4.74}, {"text": "we're at some critical point and X is", "start": 584.19, "duration": 4.47}, {"text": "equal to 12 now let me tell you", "start": 586.53, "duration": 3.99}, {"text": "something you don't we don't even have", "start": 588.66, "duration": 3.0}, {"text": "to look at the second derivative here", "start": 590.52, "duration": 3.24}, {"text": "what happens when X is equal to 12 what", "start": 591.66, "duration": 3.63}, {"text": "will happen to the volume of the box if", "start": 593.76, "duration": 5.16}, {"text": "X is equal to 12 what is the length of", "start": 595.29, "duration": 7.35}, {"text": "this base its 0 right because the length", "start": 598.92, "duration": 5.73}, {"text": "of this base is 24 minus 2x so this", "start": 602.64, "duration": 4.17}, {"text": "would be 0 this would be 0 so this this", "start": 604.65, "duration": 4.11}, {"text": "is a point where we have a volume of 0", "start": 606.81, "duration": 3.21}, {"text": "so you know that this is going to be a", "start": 608.76, "duration": 3.57}, {"text": "minimum point and if you want to verify", "start": 610.02, "duration": 4.2}, {"text": "it take the second derivative of the", "start": 612.33, "duration": 3.45}, {"text": "volume and evaluate the second", "start": 614.22, "duration": 3.63}, {"text": "derivative of the volume at 12 and you", "start": 615.78, "duration": 4.8}, {"text": "will realize that we are concave upwards", "start": 617.85, "duration": 4.95}, {"text": "and that x equals 12 is a minimum point", "start": 620.58, "duration": 5.22}, {"text": "so you already know in all probability", "start": 622.8, "duration": 6.63}, {"text": "the answer is x equals 4 and if you", "start": 625.8, "duration": 4.89}, {"text": "really wanted to verify it you could", "start": 629.43, "duration": 3.57}, {"text": "take the second derivative at x equals 4", "start": 630.69, "duration": 5.1}, {"text": "and make sure that we are concave", "start": 633.0, "duration": 4.71}, {"text": "downwards at that point right because if", "start": 635.79, "duration": 3.42}, {"text": "we want a maximum point we want to be", "start": 637.71, "duration": 2.73}, {"text": "someplace where the graph looks", "start": 639.21, "duration": 2.4}, {"text": "something like that so we're at a", "start": 640.44, "duration": 3.45}, {"text": "maximum point so what's the second", "start": 641.61, "duration": 6.12}, {"text": "derivative V prime prime of X is equal", "start": 643.89, "duration": 15.87}, {"text": "to 24 24x minus 192 and what's 24 times", "start": 647.73, "duration": 12.51}, {"text": "4 it's", "start": 659.76, "duration": 4.68}, {"text": "96 right so V prime prime V prime prime", "start": 660.24, "duration": 9.539}, {"text": "of 4 is equal to 96 right 4 times 24", "start": 664.44, "duration": 9.959}, {"text": "minus 192 G equals minus 96 so the", "start": 669.779, "duration": 6.921}, {"text": "second derivative at this point is", "start": 674.399, "duration": 5.401}, {"text": "negative which means that we are concave", "start": 676.7, "duration": 5.71}, {"text": "downwards which means that this is a", "start": 679.8, "duration": 6.09}, {"text": "maximum point and once again I challenge", "start": 682.41, "duration": 5.25}, {"text": "you to find another value of x where you", "start": 685.89, "duration": 3.99}, {"text": "get a larger volume and just to get it", "start": 687.66, "duration": 4.2}, {"text": "into it intuition how large will this", "start": 689.88, "duration": 6.48}, {"text": "box be well if X is 4 then each side is", "start": 691.86, "duration": 10.46}, {"text": "24 minus 8 this would be 16 by 16 by 4", "start": 696.36, "duration": 8.76}, {"text": "so that's that would be the optimal", "start": 702.32, "duration": 5.44}, {"text": "volume for that box hope you found that", "start": 705.12, "duration": 4.8}, {"text": "useful and I will see you in the next", "start": 707.76, "duration": 3.93}, {"text": "video where I will do another", "start": 709.92, "duration": 3.0}, {"text": "optimization problem this one is", "start": 711.69, "duration": 4.64}, {"text": "especially fun see you soon", "start": 712.92, "duration": 3.41}]