Let f : R [ ] R be a function defined by f(x) = max x, x2.

Question

Let f : R $$ \to $$ R be a function defined by
 f(x) = max {x, x2}. Let S denote the set of all points in R, where f is not differentiable.
Then :

Accepted Answer

From graph you can see,

(1) when x < 0 then y = x2 is greater than y = x. That is why for f(x) that curved part is chosen.

(2) when 0 $$ \le $$ x < 1 then y = x is greater than y = x2. That is why for f(x) part of that straight line is chosen.

(3) when x $$ \ge $$ 1 then y = x2 is greater than y = x. That is why for f(x) that curved part is chosen.

Here on the graph of f(x) there is two sharp corner at x = 0 and x = 1. As we know no function is differentiable at the sharp corner. So f(x) is not differentiable at those two sharp corner.

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