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

1 Answer
May 20, 2018

Answer:

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]}