Lebl-Basic-Analysis-I · Problem 4.2.5

The Derivative

Mathematics · mean-value-theorem-constant

Problem

Suppose

f : \mathbb{R} \to \mathbb{R}

is a function such that

|f(x) - f(y)| \leq |x - y|^2

for all

x

and

y

. Show that

f(x) = C

for some constant

C

. Hint: Show that

f

is differentiable at all points and compute the derivative.