The function f(x) = | x3 | is

Question

The function f(x) = | x3 | is (A) differentiable every where (B) continuous but not differentiable at x = 0 (C) not a continuous function (D) none of these

Tardigrade Admin · Accepted Answer

The range of the function x3 is (- ∞, ∞), and the range of f (x) is [0, ∞), f is clearly differentiable except possibly at the point x = 0. Now, clearly by definition R f '(0) = L f' (0) = 0 so that, f is differentiable at x = 0 and hence everywhere.

Q. The function $f (x) = ∣ x^{3} ∣$ is

differentiable every where

continuous but not differentiable at x = 0

not a continuous function

none of these

The range of the function $x^{3}$ is $(- \infty, \infty)$ , and the range of $f (x)$ is $[0, \infty)$ , f is clearly differentiable except possibly at the point $x = 0$ . Now, clearly by definition $R f^{'} (0) = L f^{'} (0) = 0$ so that, f is differentiable at $x = 0$ and hence everywhere.

Q. The function f(x)=∣x3∣ is