The function `g(x) =[ x+b, x < 0; cos x, x >= 0`, can be made differentiable at x = 0

Show that the function f(x)=x|x| is continuous and differentiable at x = 0

Show that the function f(x)={x^m sin(1/x) , 0 ,x != 0,x=0 is differentiable at x=0 ,if m > 1 and continuous but not differentiable at x=0 ,if 0

The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} can be made differentiable at x = 0

The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} can be made differentiable at x = 0

The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} can be made differentiable at x = 0.

The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} cannot be made differentiable at x = 0.

The function f(x)=a sin |x| +be^|x| is differentiable at x=0 when

The function f(x)=asin|x|+be^(|x|) is differentiable at x = 0 when -

Is the function [x] differentiable at x=0?