# How do you determine whether the function #f(x) = 6x^3+54x-9# is concave up or concave down and its intervals?

##### 1 Answer

Jul 17, 2015

You can study the sign of the second derivative:

#### Explanation:

You start with the first derivative:

So:

then:

set

so:

or visually:

Where

Plotting the graph you can confirm this: