# What are the global and local extrema of #f(x)=x^2 -2x +3# ?

##### 1 Answer

#### Answer:

#### Explanation:

Determine the critical points of the function, by solving the equation:

Evaluate the second derivative in this point:

As the second derivative is positive this critical point is a local minimum, and the value of the function at the minimum is:

Now consider the function:

this is a perfect square:

It follows that for

and then:

which means that in

On the other hand:

so the function is not bounded and can have no absolute maximum.

We can conclude that

graph{x^2-2x+3 [-8.375, 11.625, 0.48, 10.48]}