# Find the extreme values of #y= x^2 − 2x + 3#?

##### 3 Answers

Minimum at

#### Explanation:

To get the minimum set the derivative

equal to zero:

which solves for

Since the highest exponent in this equation is 1 it only has one solution.

By doing the second derivative

The maximums are, since the highest exponent in the original equation (2) is even and has a positive factor, at

Solution part 1 of 2: All answer for

Upper bound

#### Explanation:

The term

So to use a none mathematical term;

So

Tends to

Note that if

Also that if

Thus we write:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Foot note

As the

Solution part 2 of 2: The whole and final answer.

#### Explanation:

Given:

As the

To determine this we need the vertex (bottom of the

This will be

Looking at the given equation notice that

But

Given

Substitute

Vertex