Question

Verify L.M.V for the function ? $f\left(x\right)=\left\{\begin{array}{cc}2+x^3& x\le 1\\ 3x& x>1\end{array}\right\}on[-1,2]$

Answer 1

$\underset{x\to 1}{lim}{f}^{\prime }\left(x\right)=2+3(1{)}^2=5$

$\underset{x\to 1}{lim}+f^{\prime }\left(x\right)=3$

$\therefore$ Not Differentiable at $x=1$