# How do use the first derivative test to determine the local extrema #x^2+1#?

##### 1 Answer

#### Answer:

You can use three easy steps:

#### Explanation:

**First** you evaluate the derivative of your function:

**Second** you set it equal to zero (so you get the

or

**Third** we need to understand if it is a max or min so we set the derivative bigger than zero:

you get that

this means that the derivative is bigger than zero (function going up) when

Your minimum has coordinates

Graphically:

graph{x^2+1 [-10, 10, -5, 5]}

you can see that for