# How do you ise interval notation indicate where f(x) is concave up and concave down for #f(x)=x^(4)-6x^(3)#?

##### 1 Answer

#### Explanation:

What you want to do is find the second derivative using the power rule:

The first derivative is:

The second derivative is:

What you want to do now is factor it and set it equal to zero:

Now you make a test interval from:

You test values from the left and right into the second derivative but not the exact values of

If you get a negative number then it means that at that interval the function is concave down and if it's positive its concave up.

If done so correctly you should get that:

You should also note that the points

Attached below is a picture that may help you:

The graph may also help you:

graph{x^4-6x^3 [-147.3, 145, -125.6, 20.5]}