How to find $ f(6)$ given the following functional equation .

Let $f:\Bbb R\to\Bbb R$ be a function such that $\lvert f(x)-f(y)\rvert\le 6\lvert x-y\rvert^2$ for all $x,y\in\Bbb R$. If $f(3)=6$ then $f(6)$ equals:

how to calculate this ? facing problem with the inequality up there .

Answer

Hint: $f$ is differentiable at all points, and its derivative can be calculated explicitly.