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

May 20, 2018

Maximum value : $\infty$ , minimum value is $1$

#### Explanation:

$f \left(x\right) = {x}^{2} - 2 x + 2$ . This is equation of parabola opening

up since coefficient of ${x}^{2}$ is positive , hence maximum value is

$\infty$ and there is minimum value. f^'(x)= 2 x -2 ; f^('')(x) =2

for critical point ${f}^{'} \left(x\right) = 0 \therefore 2 x - 2 = 0 \therefore x = 1$

Since ${f}^{' '} \left(x\right) > 0 \therefore f$ has local minimum at x=1#

The minimum value is $f \left(1\right) = {1}^{2} - 2 \cdot 1 + 2 = 1 - 2 + 2 = 1$

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