Question

Find the maximum and minimum value if any of the function f is given by f(x)=x square,x€R

Answer 1

function is f(x) = x² , $x\in R$

you know about graph of x² ? because x² is an even function therefore graph of x² is symmetrical about y- axis. also graph is parabolic and it is vertically upward as shown in figure. so, x² gain minimum at x = 0 as you can see .
hence, minimum value of x² = 0
maximum doesn't possible for f(x).

Well, you can get it by analytical method
differentiate with respect to x,
f'(x) = 2x
now, f'(x) = 0 => x = 0
f"(x) = 2 > 0 , f(x) gains minimum at x = 0
so, minimum value of f(x) = 0