Differentiability and Continuity

Question

Let $m$ and $n$ be the numbers of points at which $f(x) = \max\{x, x^3, x^5, \dots, x^{21}\}$ for $x \in \mathbb{R}$ is not differentiable and not continuous, respectively. What is the value of $m + n$?

Answer 1

For x =

 -infinity to -1 ,   f(x) = x     ( as it is the greatest in this range , other have more power so bigger negative value)

        -1. to 0 ,  f(x) = x^21.

          0 to 1  , f(x) = x

and 1 to  infinity  f(x) = x^21

So, given function is continuous every whare and is not differentiable at -1, 1, 0.

so m=3 and n=0 .

Hence m+n = 3