If $f(x) = |2x+5|, $ then $f(x)$ is :
Answer & explanation
Correct answer: option 4
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 $-\frac{5}{2}$