The extreme value of a function is its value at the point where the value of the first derivative is equal to 0.

f(x) = x^2 - 2x + 2

=> f'(x) = 2x - 2

2x- 2 = 0

=> x = 1

At x = 1, f(x) = 1^2 - 2 + 2 = 1

**The extreme value of the given function is 1.**