If $f(x) = |2x+5|, $ then $f(x)$ is :

Continuous and non differentiable at $x=\frac{-5}{2}$

The correct answer is Option (4) → Continuous and non differentiable at $x=\frac{-5}{2}$

$f(x)=\left\{\begin{matrix}2x+5&x≥-5/2\\-2x-5&x<-5/2\end{matrix}\right.$

$\underset{x→-\frac{5}{2}}{\lim}=0=f(-\frac{5}{2})$ ⇒ f is continuous at $-\frac{5}{2}$

$f'(x)=\left\{\begin{matrix}2&x≥-5/2\\-2&x<-5/2\end{matrix}\right.$

$LHD=-2$, $RHD=2$

$LHD≠RHD$

f is not differentiate at $-\frac{5}{2}$