Integration/Function with positive derivative/Extrema of partial areas/Exercise

Let

$f\colon [0,1]\longrightarrow \mathbb {R} _{+}$

be a differentiable function with ${}f'(x)>0$ for all ${}x>0$. For what points ${}t\in [0,1]$ does the area of the hatched surface have a local extremum?

Is it a minimum or a maximum?

Create a solution