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Merged
merged 9 commits into from
Oct 13, 2025
Merged

update AD5 checkit per CheckIt - AD5 and AD6. #52 #814

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f149001
update AD5 checkit per CheckIt - AD5 and AD6. #52
cg2wilson Jun 11, 2025
84c16a9
update ad6 checkit per CheckIt - AD5 and AD6. #52
cg2wilson Jun 11, 2025
7ca8443
Merge branch 'main' into cg2wilson-ad5ad6-checkit
StevenClontz Oct 3, 2025
db819fb
Update source/calculus/exercises/outcomes/AD/AD5/template.xml
cg2wilson Oct 5, 2025
83eff21
fixed spatext syntax in AD5 and AD6
cg2wilson Oct 7, 2025
a807572
remove <p> tags around <list>s
cg2wilson Oct 7, 2025
bf93358
Update source/calculus/exercises/outcomes/AD/AD6/template.xml
cg2wilson Oct 7, 2025
21833b5
Update source/calculus/exercises/outcomes/AD/AD6/template.xml
cg2wilson Oct 7, 2025
b80448c
Update source/calculus/exercises/outcomes/AD/AD6/template.xml
cg2wilson Oct 7, 2025
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161 changes: 130 additions & 31 deletions source/calculus/exercises/outcomes/AD/AD5/template.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -2,58 +2,157 @@
<knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
<intro>
<p>
For <m>\displaystyle f(x) = {{f}} </m>, identify the regions for which <m>f(x)</m> is increasing and decreasing (if any). Additionally, identify and classify all local extrema.
For <m>\displaystyle f(x) = {{f}} </m>, identify the open intervals for which <m>f(x)</m> is increasing and decreasing (if any). Additionally, identify and classify all local extrema.
</p>
</intro>

<outtro>
<!-- {{#case1}} -->
<p>
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is neither a max nor min.
</p>
<list>
<item>
<p>

We have that <m>\displaystyle f'(x) = {{fp}}</m>.
</p>
</item>
<item>
<p>

When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
</p>
</item>
<item>
<p>

When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
</p>
</item>
<item>
<p>
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is neither a max nor min.
</p>
</item>
</list>

<!-- {{/case1}} -->

<!-- {{#case2}} -->
<p>
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is a local minimum and a critical point <m>{{cp2}}</m> is a local maximum.
</p>
<list>
<item>
<p>

We have that <m>\displaystyle f'(x) = {{fp}}</m>.
</p>
</item>
<item>
<p>

When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
</p>
</item>
<item>
<p>

When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
</p>
</item>
<item>
<p>

When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is a local minimum and a critical point <m>{{cp2}}</m> is a local maximum.
</p>
</item>
</list>
<!-- {{/case2}} -->


<!-- {{#case3}} -->
<p>
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There are no critical points.
</p>
<list>
<item>
<p>

We have that <m>\displaystyle f'(x) = {{fp}}</m>.
</p>
</item>
<item>
<p>

When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
</p>
</item>
<item>
<p>

When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
</p>
</item>
<item>
<p>

When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There are no critical points.
</p>
</item>
</list>
<!-- {{/case3}} -->


<!-- {{#case4}} -->

<!-- {{#odd}} -->
<p>
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is a local minimum.
</p>
<list>
<item>
<p>

We have that <m>\displaystyle f'(x) = {{fp}}</m>.
</p>
</item>
<item>
<p>

When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
</p>
</item>
<item>
<p>

When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
</p>
</item>
<item>
<p>

When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is a local minimum.
</p>
</item>
</list>
<!-- {{/odd}} -->
<!-- {{#even}} -->
<p>
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There are critical points <m>{{cp1}}</m> which is a local maximum and <m>{{cp2}}</m> which is a local minimum.
</p>
<list>
<item>
<p>

We have that <m>\displaystyle f'(x) = {{fp}}</m>.
</p>
</item>
<item>
<p>

When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
</p>
</item>
<item>
<p>

When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
</p>
</item>
<item>
<p>

When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There are critical points <m>{{cp1}}</m> which is a local maximum and <m>{{cp2}}</m> which is a local minimum.
</p>
</item>
</list>
<!-- {{/even}} -->


Expand Down
158 changes: 129 additions & 29 deletions source/calculus/exercises/outcomes/AD/AD6/template.xml
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -2,52 +2,152 @@
<knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
<intro>
<p>
For <m>\displaystyle f(x) = {{f}} </m>, identify the regions where <m>f(x)</m> is concave up and concave down (if any) as well as all inflection points.
For <m>\displaystyle f(x) = {{f}} </m>, identify the open intervals where <m>f(x)</m> is concave up and concave down (if any) as well as all inflection points.
</p>
</intro>

<outtro>
<!-- {{#case1}} -->
<p>
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{change4}}. There are inflection points <m>{{ip1}}</m> and <m>{{ip2}}</m>.
</p>
<list>
<item>
<p>

We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
</p>
</item>
<item>
<p>

When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
</p>
</item>
<item>
<p>

When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
</p>
</item>
<item>
<p>

When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
</p>
</item>
<item>
<p>

When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{concave4}}. There are inflection points <m>{{ip1}}</m> and <m>{{ip2}}</m>.
</p>
</item>
</list>
<!-- {{/case1}} -->

<!-- {{#case2}} -->
<p>
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{change4}}. There are inflection points <m>{{ip1}}</m>, <m>{{ip2}}</m> and <m>{{ip3}}</m>.
</p>
<list>
<item>
<p>

We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
</p>
</item>
<item>
<p>

When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
</p>
</item>
<item>
<p>

When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
</p>
</item>
<item>
<p>

When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
</p>
</item>
<item>
<p>

When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{concave4}}. There are inflection points <m>{{ip1}}</m>, <m>{{ip2}}</m> and <m>{{ip3}}</m>.
</p>
</item>
</list>
<!-- {{/case2}} -->


<!-- {{#case3}} -->
<p>
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{change4}}. There is an inflection point <m>{{ip1}}</m>.
</p>
<list>
<item>
<p>

We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
</p>
</item>
<item>
<p>

When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
</p>
</item>
<item>
<p>

When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
</p>
</item>
<item>
<p>

When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
</p>
</item>
<item>
<p>

When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{concave4}}. There is an inflection point <m>{{ip1}}</m>.
</p>
</item>
</list>
<!-- {{/case3}} -->


<!-- {{#case4}} -->

<p>
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
When <m>{{cc2}} &lt; x, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
There is an inflection point <m>{{ip1}}</m>.
</p>
<list>
<item>
<p>

We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
</p>
</item>
<item>
<p>

When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
</p>
</item>
<item>
<p>

When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
</p>
</item>
<item>
<p>

When <m>{{cc2}} &lt; x, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
</p>
</item>
<item>
<p>

There is an inflection point <m>{{ip1}}</m>.
</p>
</item>
</list>
<!-- {{/case4}} -->


Expand Down