Let $f$ be continuous on $[0,10]$ with $f(0)=3$ and $f(10)=7$. Suppose $f'(x)>0$ on $(0,4)$ and $f'(x)<0$ on $(4,10)$. Which statement must be true?

Core Concept

$f$ increases on $(0,4)$ and decreases on $(4,10)$, so $f(4)$ is greater than every other value of $f$ on $[0,10]$. That makes $x=4$ the absolute maximum.