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

Answer 1

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]}

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Answer 2

The function ( f(x) = x^2 - 2x + 2 ) has a minimum value.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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