$g'(t)\geq 0$ for all values of $t$.
The function is differentiable and satisfies the conditions above. Let $F$ be the function given by $F(x)=\int_0^x g(t) dt$. What must be true?
$F$ has a local minimum at $F=20$.
This is the question and answer that I was given. (It was a multiple choice question, I just included the correct answer.) I know this is correct, but why is it so? How do I understand this based on the given information?