Let `f : R to R ` be a function defined by `f(x) = max. {x, x^(3)}`. The set of all points where `f(x) ` is NOT differenctiable is
(a) `{-1, 1}`
(b) `{-1, 0}`
(c ) `{0, 1}`
(d) ` {-1, 0, 1}`

Explanation

We have `f(x) = max. {x, x^(3)}`
Draw the graphs of `y=x and y= x^(3)`

Graph of `y = f(x)` is combination of the combination of the blue and red-lined graphs.
From the graph, `y= f(x) ` is non-differentiable at `x=-1, x=0 and x=1`.