Differentiable functions/Larger and derivative larger/Exercise

Let

$f,g\colon \mathbb {R} \longrightarrow \mathbb {R}$

be two differentiable functions. Let ${}a\in \mathbb {R}$. Suppose we have that

$f(a)\geq g(a){\text{ and }}f'(x)\geq g'(x){\text{ for all }}x\geq a.$

Prove that

$f(x)\geq g(x){\text{ for all }}x\geq a.$

Create a solution