The function!

Calculus Level 3

Let f:RRf: \mathbb {R \to R} be a function such that for all x,yRx , y \in \mathbb R

f(x)f(y)6xy2\large \left| f(x) - f(y)\right| \le 6\left|x - y\right|^2

If f(3)=6f(3) = 6 then find f(6)f(6).

Notation: |\cdot| denotes the absolute value function.

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