From 766180f2ebcad61dcb3adcf925ac1a433981d2f4 Mon Sep 17 00:00:00 2001
From: pfatheddin <156558883+pfatheddin@users.noreply.github.com>
Date: Mon, 18 Mar 2024 20:42:54 -0400
Subject: [PATCH] Update maxMinSecondDerivativeTest4.tex

https://ximera.osu.edu/mooculus/maximumsAndMinimums/exercises/exerciseList/maximumsAndMinimums/exercises/maxMinSecondDerivativeTest4


There are two critical points. It is missing 4 where it does not exist. I added this and added a hint saying we can't apply the second derivative test on it.
---
 .../exercises/maxMinSecondDerivativeTest4.tex            | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

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}