Question

Does the function `f(x) = x^2 - 2x + 2` have a maximum or minimum value?

Answer 1

Maximum value : `oo` , minimum value is `1`

Explanation:

`f(x) = x^2-2 x+2` . This is equation of parabola opening

up since coefficient of `x^2` is positive , hence maximum value is

`oo` and there is minimum value. `f^'(x)= 2 x -2 ; f^('')(x) =2`

for critical point `f^'(x)= 0 :. 2 x-2= 0 :. x=1`

Since `f^('')(x) >0 :. f` has local minimum at x=1#

The minimum value is `f(1)= 1^2-2*1+2=1-2+2=1`

graph{x^2-2 x +2 [-10, 10, -5, 5]}