`f(x) = |x|` differentiability check at `x= 0`

Show that f(x)=|x| is not differentiable at x=0.

Show that f(x)=|x| is not differentiable at x=0.

Show that f(x)=|x| is not differentiable at x=0.

Show that f(x)=|x| is not differentiable at x=0 .

Prove that f (x) = x |x| is differentiable at x =0 and find f'(0) also find f '(x) on R.

If f(x)={xe^-[1/(|x|)+1/x]; x != 0; 0;x=0 Prove that f(x) is not differentiable at x = 0

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

Check the differentiability of the following at x = 0 (a) cos(|x|) + |x|, (b) sin(|x|) - |x|.

Assertion (A) : f(x) = xsin ((1)/(x)) is differentiable at x=0 Reason (R): F(x)is continuous at x=0