MHT CET 2017 Math Solved Paper

(a) We have, f(x) = {

x	for‌x≤0
0	for‌x>0

LHL at x = 0 =

lim

x→0−

f(x)=

lim

x→0

x
and RHL at x = 0 =

lim

x→0+

f(x)=

lim

x→0

0 = 0
Now,f(0) = 0
So, LHL= RHL = f(0)
Hence, f(x) is continuous at x = 0
Here, f′(x) = 1 for x ≤ 0,
0 for x > 0
Thus, f(x) is not differentiable at x = 0