diff --git a/maximumsAndMinimums/exercises/maxMinSecondDerivativeTest4.tex b/maximumsAndMinimums/exercises/maxMinSecondDerivativeTest4.tex index 39241711f..16018f0ab 100644 --- a/maximumsAndMinimums/exercises/maxMinSecondDerivativeTest4.tex +++ b/maximumsAndMinimums/exercises/maxMinSecondDerivativeTest4.tex @@ -16,14 +16,17 @@ \begin{exercise} -The function $f(x) = x\sqrt{4-x}$ has only one critical point, $x=a$. +The function $f(x) = x\sqrt{4-x}$ has two critical points $a, b$ in ascending order, $$ -a = \answer{8/3} +a = \answer{8/3} \textrm{ and } b = \answer{4} $$ -$f''(a)$ is \wordChoice{\choice{positive} \choice[correct]{negative}}, so $x=a$ is a local \wordChoice{\choice[correct]{max} \choice{min}}. +$f''(a)$ is \wordChoice{\choice{positive} \choice[correct]{negative}}, so $x=a$ is a local \wordChoice{\choice[correct]{max} \choice{min}}. +\begin{hint} +Note that we cannot apply the second derivative test on $x =b$, since $f''(b)$ does not exist. +\end{hint} \end{exercise} \end{document}