# How do you determine whether the function #f(x)=3x^5 - 20x^3# is concave up or concave down and its intervals?

##### 1 Answer

We use the second derivative test and find that

f is concave down on

#### Explanation:

For concavity we use the second derivative test.

This second derivative equals zero if

These are then the possible inflection points of the function where concavity could change.

We now investigate the sign of the second derivative around these points :

*_**_**_** -root2 __ 0 ___root2 __*

F''(x) ; - + - +

graph{3x^5-20x^3 [-10, 10, -5.21, 5.21]}