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.
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):
Now we have to calculate the equation of the first derivative:
We'll divide by 2:
x-1 = 0
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).