Continuous Calculus-2

True or False

Suppose $f$ is a real-valued continuous function defined on $[-2, 2]$ and is three times differentiable in $(-2, 2)$ .

If $f(2) = -f(-2) = 4$ and $f'(0)=0$ , then there exists $x \in (-2, 2)$ such that $f'''(x) ≥ 3$

Note: $f'''(x)$ means differentiated three time w.r.t $x$