Condition of extremum

Condition 1

which of the folloiwng function has point of extremum at x =0?

The poins of extremum of phi(x)=int_(1)^(x) e^(-t^(2)//2) (1-t^(2))dt are

For f(x) = sin x - x^(2) + 1 , check weather the function is increasing, decreasing or has a point of extremum ?

Investigate the following functions for an extremum at the point x = 0 : y = cos x -1 +(x^(2))/2

The number of points of extremum of the function f(x)=(x-2)^(2/3)(2x+1) is

Investigate the following functions for an extremum at the point x = 0: f(x) = {:{(e^(1//x)", if "x !=0 ),(0", if "x=0):}