-1
$\begingroup$

I have problems with the following task:

Let $I \subset \mathbb R $ be an unpredicted interval, and let $F, G: I \to \mathbb R$ be continuously differentiable.

$F'(x) \leq G'(x) $ for all $x \in I$ and there is an $a \in I$ with $F(a) \leq G(a)$. Prove, that for all $x \in I$ with $x \geq a$, $F(x) \leq G(x)$ is also valid.

Do you have ideas how to prove that?

Thank you.

  • 0
    What do you mean by "unpredicted"? – 2017-01-25
  • 0
    Are you still here? – 2017-01-27

1 Answers 1

0

Hint:

Mean value theorem applied to $F-G$.