AMU Engineering 2020 solved paper Solved Paper

We have,
f(x)={

−x	‌	−1≤x<0
1−x	‌	0≤x<1
x	‌	1≤x<2
1+x	‌	2≤x<3
5	‌	x=3.

Clearly, f(x) is discontinuous at x=0,1,2 and 3 . So, it is not differentiable at these points.
At x=−1, we have

lim

x→−1+

f(x)=

lim

x→−1+

−x=1=f(−1)
So, it is continuous at x=−1.
Also, (RHD at x=−1)=−1 (a finite number).
Therefore, f(x) is differentiable at x=−1.