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.
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