Verify Lagrange's Mean Value Theorem for the function : \[ f(x)=\le...

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Verify Lagrange's Mean Value Theorem for the function :
\[
f(x)=\left\{\begin{array}{ccc}
2+x^{3} & \text { if } & x \leq 1 \\
3 x & \text { if } & x1
\end{array} \text { on }[-1,2] .\right.
\]
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