Question

The function f(x) = x | x |, x ∈ R is differentiable ______.

विकल्प

• only at x = 0

• only at x = 1

• in R

• in R – {0}

Answer 1

The function f(x) = x | x |, x ∈ R is differentiable in R.

Explanation:

f(x) = x | x |, x ∈ R is differentiable.

= `{{:(x^2 ≥ 0,),(-x^2",", x < 0):}` if x ≠ 0, then the function is quadratic so is differentiable. The only point to consider is 0. But since both x² and – x² have same derivative at 0, then it follows that f is differentiable at 0.