The set of all points where the function f (x) = 2x| x|is differentiable is

Step-by-step solution

f(x) = 2x | x | f(x)= array cc 2 x^2 & , x 0 -2 x^2 & , x < 0 array . Since, f(x) is a polynomial function, hence it will be differentiable everywhere. We need to check only at x = 0. LHD f^ (0⁻ )= _ h 0⁻ f(0+h)-f(0) h = _ h 0⁻ -2 (h^2 )-0 h =0 RHD f^ (0⁺ )= _ h 0⁺ f(0+h)-f(0) h = _ h 0⁺ 2 h^2-0 h = _ h 0⁺ 2 h=0 f(x) is differentiable in (- , )