diff --git a/meanValueTheorem/exercises/GBranchQ6AU15.tex b/meanValueTheorem/exercises/GBranchQ6AU15.tex index ee6e40a78..cd70c0a46 100644 --- a/meanValueTheorem/exercises/GBranchQ6AU15.tex +++ b/meanValueTheorem/exercises/GBranchQ6AU15.tex @@ -11,34 +11,7 @@ Let $f(x) = 20 + 8x^2 - x^4$.\\ Find the global maximum and global minimum values of $f$ on the closed interval $[-3,3]$ and find the x-coordinates of the points where they are attained. -\begin{hint} - First, we have to compute $f'(x)$. - -$f'(x) = \answer{16x-4x^3}=-4x(\answer{x^2-4})=-4x(x-\answer{2})(x+\answer{2})$. - -Complete the statement below. - -The x-coordinates of all critical points of $f$ (from left to right) are $a=\answer{-2}$, $b=\answer{0}$, and $c=\answer{2}$. -\end{hint} -\begin{hint} -Now, we evaluate the function $f$ at the end points and at the critical points. -$$ -f(-3) = \answer{11} -$$ -$$ -f(3) = \answer{11} -$$ -$$ -f(a) = \answer{36} -$$ -$$ -f(b) = \answer{20} -$$ -$$ -f(c) = \answer{36} -$$ -Now we compare these values and answer the question. -\end{hint} + The global maximum value of $f$ on the interval $[-3,3]$ is $\answer{36}$ and it is attained at $x=\answer{-2}$ and at $x=\answer{2}$ . The global minimum value of $f$ on the interval $[-3,3]$ is $\answer{11}$ and it is attained at $x=\answer{-3}$ and at $x=\answer{3}$ .