Is f(x) = |x-1|+|x-2| differentiable at x=2?

If f(x) = 3(2x + 3)^(2//3) + 2x + 3 , then: (a) f(x) is continuous but not differentiable at x = - (3)/(2) (b) f(x) is differentiable at x = 0 (c) f(x) is continuous at x = 0 (d) f(x) is differentiable but not continuous at x = - (3)/(2)

Prove that the greatest integer function defined by f(x) = [x], 0

if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} a. f is continuous at x = 0 b. f is continuous at x = 0 but not differentiable at x = 0 c. f is differentiable at x = 0 d. f is not continuous at x = 0

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

Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differentiable both at x = 0 and at x = 2 b. differentiable at x = 0 but not differentiable at x = 2 c. not differentiable at x = 0 but differentiable at x = 2 d. differentiable neither at x = 0 nor at x = 2

if f(x) = {{:(x^2, x le 1),(ax + b ,x gt 1):} is differentiable at x = 1 . Find the values of a and b.

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

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not differentiable at (a)-1 (b)0 (c)1 (d)2