Question

F(x) =

x^2/
(x^2 − 9)

Where is the auction increasing and decreasing?
Critical numbers= 2

Answer 1

Increasing: on the interval of x: (-∞, 0)

Decreasing: on the interval of x: (0, ∞)

Explanation:

See attached photos, one is done using calculus, the other is done using the graph. (I'm not sure which level of math you are in)

*For the graph, you can see that f(x) is always increasing from (-∞, 0), and always decreasing from (0, ∞)

Answer 2

Explanation:

The first thing to do is get a graph of the function if you can.

The graph helps you see the following.

1. The critical points are at +/- 3
2. The graph is increasing from -∞ ≤x<-3 Watch that you do not include - 3
3. The graph is increasing form -3<x<0
4. The graph is decreasing from 0<x<3
5. The graph is decreasing from 3<x<∞