Differentiable functions/Higher intersection with diagonal/Derivation/Exercise

Let

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

be a continuously differentiable function, and suppose that its graph intersects the diagonal in at least two points ${}P\neq Q$. Show that the graph of the derivative ${}f'$ has an intersection point with the line given by

${}y=1$.

Create a solution