Differentiable function/Same derivation/Same point/Exercise

Let

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

be differentiable functions. Let ${}a\in \mathbb {R}$ be a point, and suppose that

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

Show that

$f(x)=g(x){\text{ for all }}x{\text{ gilt}}.$

Create a solution