Show that the function `f(x) = |x-1| +1| for all x in R`, is not differentiable at x = -1 and x =1

Prove that the function f given by : f(x) = |x-1|, x in R is not differentiale at x =1

Prove that the function f given by f(x) = |x-1|, x in R, x=1 is not differentiable at x = 1.

Show that the function 'f' given by: f(x) = |x| + |x-1|, x in R is continuous both at x = 0 and x=1

Show that the function 'f' given by: f(x) = |x-1|+|x-2|, x in R is continuous both at x =1 and x=2

The function f(x) = |x| + |x-1| + |x-2| is continuous but not differentiable at for all x in R x=-1 and x=1

Show that the function f(x) = |x + 1| + | x - 1| is continuous at x = -1 , x = 1

Show that the function f (x) = (x)/(1+|x|) is a strict increasing function.

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