Given the function f(x)=-x^3-6x^2-9x determine all intervals on which f' is decreasing.

Question

Answer 1

To determine the intervals on which

is decreasing, we first need to find the derivative of

, which is

. Then, we can find the critical points by setting

and solving for

. Finally, we can use these critical points to determine the intervals on which

is decreasing.Step 1: Find the derivative of

.

Step 2: Find the critical points by setting

and solving for

.

or

Step 3: Determine the intervals on which

is decreasing.We can use the critical points to divide the number line into three intervals:

,

, and

. We can then test a point from each interval in

to determine whether

is increasing or decreasing in that interval.For

, let's choose

:

For

, let's choose

:

Therefore,

is decreasing on the intervals

and

.

Question