Question

Let f : R → R be a function defined by f (x) = max {x, x³}. The set of all points where f(x) is not differentiable, is

(a) {-1, 1}

(b) {-1, 0}

(c) {0, 1}

(d) {-1, 0, 1}

Answer 1

Correct option (d) {-1, 0, 1}

Explanation :

Given, f(x) = max {x, x³}. considering the graph separately,

y = x³ is odd order parabola and y = x is always intersect at (1, 1) and (-, -1).

The point of consideration are