diff --git a/meanValueTheorem/exercises/meanValueTheorem3.tex b/meanValueTheorem/exercises/meanValueTheorem3.tex index 704b0cfe6..160c0f9dd 100644 --- a/meanValueTheorem/exercises/meanValueTheorem3.tex +++ b/meanValueTheorem/exercises/meanValueTheorem3.tex @@ -42,12 +42,9 @@ $02$. +Since the function $g$ satisfies the conditions of the Mean value theorem (MVT), there exists a points $c$ in $(3,5)$ such that $g'(c)=\answer{3}$. Thus, $g'(c)>2$. \end{hint} + \begin{multipleChoice} \choice{True} \choice[correct]{False} @@ -55,13 +52,9 @@ $00$ on $(3,5)$, the function $g$ is increasing on the interval $(3,5)$. +Since $g'(x)>0$ on $(3,5)$, the function $g$ is increasing on the interval $(3,5)$. Thus, $g(x)\le g(5)$, for all $x$ in $(3,5)$. \end{hint} -\begin{hint} -Since the function $g$ is increasing (and continuous on $[3,5]$) on the interval $(3,5)$, it follows that - $g(x)\le g(5)$, for all $x$ in $(3,5)$. -\end{hint} \begin{multipleChoice} \choice[correct]{True} \choice{False} @@ -70,4 +63,4 @@ \end{exercise} -\end{document} \ No newline at end of file +\end{document}