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

Show that f(x)=x^(1/3) is not differentiable at x=0

Show that f(x) = |x| sin x is differentiable at x=0.

Show that f(x)=(x)^(1/3) is not differentiable at x=0.

Show that f(x)=x^(1//3) is not differentiable at x=0 .

Show that f (x) = [x] is not differentiable at x = 1 .

Show that f(x)=(x^(1))/(3) is not differentiable at x=0.

If function f(x)=|x-3|+|x-4| , then show that f(x) is not differentiable at x=3 and x=4 .

(i) Show that f (x) = x ^( 4//3) is differentiable at x = 0 , and hence find f ' (0) . (ii) Show that g(x) = x ^( 3//2) is not differentiable at x = 0

If f(x) = {:{(xsin(1/x),xne0),(0,x=0):} Show that 'f' is not differentiable at x =0

f(x)= x^(3) sgn(x). Show that f(x) is differentiable at x=0.