Question 49
Consider $f : [a, b] \to [a, b]$ a differentiable function, such that $f'$ is continuous and positive. Show that there is a point $c \in (a, b)$ such that
$$
f(f(b)) - f(f(a)) = (f'(c))^2 (b - a).
$$
$$
f(f(b)) - f(f(a)) = (f'(c))^2 (b - a).
$$