Let m and n be the number of points at which the function f( x )= x , x ^3, x ^5, ., x ²¹ , x R , is not differentiable and not continuous, respectively. Then m + n is equal to ________ .

Step-by-step solution

f(x)= array cc x, & x -1 x²¹, & -1 x 0 x, & 0 x 1 x²¹, & x 1 array . f(x) is continuous everywhere. aligned & n =0 & f ^ ( x )= array cc 1, & x -1 21 x ²⁰, & -1 x 0 1, & 0 x 1 21 x ²⁰, & x 1 array . aligned f ( x ) is non-differentiable at x =-1,0,1 aligned & m =3 & ~m + n =3 aligned