Differentiable functions/Larger and derivative larger/Exercise

Let

$f,g:ℝ⟶ℝ$

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

$f(a)\ge g(a)\text{ and }{f}^{\prime }(x)\ge g^{\prime }(x)\text{ for all }x\ge a.$

Prove that

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

Create a solution