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

Question

10874 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-20T12:57:04

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

$f(x) = x^2-2 x+2$ . 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]}

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