Question

prove that f(x) = |x| +|x-1| is not differentiable at x = 1
answer me fast pl​

Answer 1

Step-by-step explanation:

We have to check the differentiability at x = 1

Here, f(1) = 1 − 1 = 0 Hence, f(x) is not differentiable

Answer 2

Answer:

he given function is f(x)=∣x−1∣,x∈R.

It is known that a function f is differentiable at point x=c in its domain if both

lim h→0−​f(c+h)−f(c) / h​ and limh→0+​hf(c+h)−f(c)​ are finite and equal.

To check the differentiable of the function at x=1,

Consider the left hand limit of f at x=1

lim h→0−​∣1+h−1∣−∣1−1∣ / h ​=limh→0−​∣h∣/h​=limh→0−=−h​/h=−1

Consider the right hand limit of f at x−1

lim h→0+​∣1+h−1∣−∣1−1∣/h​=limh→0+​h/h​=1

Since the left and right hand limits of f at x=1 are not equal, f is not differentiable at x=1.