Ok, I see that some max/min situation exists because the 1st derivative is equal to \(\displaystyle 0\). What else can be observed? 
Let \(\displaystyle F\) be a differentiable function defined on the closed interval \(\displaystyle [a,b]\) and let \(\displaystyle c\) be a point in the open interval \(\displaystyle (a,b)\) such that:
\(\displaystyle f ' (c) = 0\)
\(\displaystyle f ' (x) > 0\) when \(\displaystyle a \leq x < c\)
\(\displaystyle f ' (x) < 0\) when \(\displaystyle c < x \leq b\)
Answer: \(\displaystyle f(c)\) is an absolute maximum value of \(\displaystyle f \) on \(\displaystyle [a,b] \)
Let \(\displaystyle F\) be a differentiable function defined on the closed interval \(\displaystyle [a,b]\) and let \(\displaystyle c\) be a point in the open interval \(\displaystyle (a,b)\) such that:
\(\displaystyle f ' (c) = 0\)
\(\displaystyle f ' (x) > 0\) when \(\displaystyle a \leq x < c\)
\(\displaystyle f ' (x) < 0\) when \(\displaystyle c < x \leq b\)
Answer: \(\displaystyle f(c)\) is an absolute maximum value of \(\displaystyle f \) on \(\displaystyle [a,b] \)
