Write the number of points where f(x) = |x| + |x – 1| is continuous but not differentiable.

Question

Philoid · Accepted Answer

Given f(x) = |x|+|x – 1|

For x<0,

f(x) = -2x+1 which being a polynomial function is continuous and differentiable.

For x € (0, 1),

f(x) = 1 which being a constant function is continuous and differentiable.

For 1

f(x) = 2x - 1 which being a polynomial function is continuous and differentiable.

So, the possible points where function is continuous but not differentiable are 0 and 1.

LHD (at x = 0):

RHD (at x =0):

∵ LHD ≠RHD

So, function is not differentiable at x =0.

Similarly,

LHD at x =1,

RHD at x =1,

∵ LHD ≠RHD

So, function is not differentiable at x =1.

The number of points where f(x) = |x| + |x – 1| is continuous but not differentiable are two i.e. x = 1 and x = 0.