Let K be the set of all real values of x , where the function f (x)= |x|-|x|+2(x- ) |x| is not differentiable. Then the set K is

Step-by-step solution

aligned f (x) & = |x|-|x|+2(x- ) |x| f (x) & = x-x+2(x- ) x, x 0 & =- x+x+2(x- ) x, x 0 aligned Now, aligned f ^ (x) & = x-1-2(x- ) x+2 x, x 0 & =- x+1-2(x+ ) x+2 x, x 0 f (0⁺ ) & = 0-1-2(0- ) 0+2 0=2 f (0⁻ ) & =- 0+1-2(0- ) 0+2 0=2 f ^ (0⁺ ) & = f ^ (0⁻ )=2 aligned f (x) is differentiable at x=0 f (x) is differentiable everywhere. k =