Determine the extreme value of the function x^2-2x+2.

To establish the extreme value of a function, we'll have
to calculate the first derivative of the function.

Let's
find the first derivative of the function
f(x):

f'(x)=( x^2-2x+2)'=(x^2)'-(2x)'+(2)'

f'(x)=2x-2

Now we
have to calculate the equation of the first
derivative:

2x-2=0

We'll
divide by 2:

x-1 =
0

x=1

That means that the
function has an extreme point, for the critical value
x=1.

f(1) = 1^2 - 2*1 + 2

f(1)
= 1-2+2

We'll eliminate like
terms:

f(1) =
1

The extreme point of the function is a
minimum point whose coordinates are: (1 ; 1).