If f(x)= cases -x- 2 ,&x - 2 - x,&- 2 1 cases which of the following statements are…

MATHEMATICS · Multi correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

f(x)=\begin{cases}-x-\frac{\pi}{2},&x\leq-\frac{\pi}{2}\\-\cos x,&-\frac{\pi}{2}<x\leq0\\x-1,&0<x\leq1\\\ln x,&x>1\end{cases}

which of the following statements are correct? (1)

f(x)

is continuous at

x=-\frac{\pi}{2}

(2)

f(x)

is not differentiable at

x=0

(3)

f(x)

is differentiable at

x=1

(4)

f(x)

is differentiable at

x=-\frac{3}{2}