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# Verify Lagrange's theorem for the following function;$f(x)=x^{\large\frac{2}{3}}[-2,2]$

Note: This is part 4th of a 5 part question, split as 5 separate questions here.

Toolbox:
• Lagrange's Mean Value Theorem :
• Let $f(x)$ be a real valued function that satisfies the following conditions.
• (i) $f(x)$ is continuous on the closed interval $[a,b]$
• (ii) $f(x)$ is differentiable in the open interval $(a,b)$
• (iii) $f(a)=f(b)$
• Then there exists atleast one value $c \in (a,b)$ such that $f'(c)=0$
$f(x)=x^{\large\frac{2}{3}}$ is $[-2,2]$ $f(x)$ is continuous