Question

p(x) is increasing on the interval (-5,1] and decreasing on the interval [1,∈ [infinity] ). p(x) is concave up on the interval (-5,-2) and concave down on the interval (-2,∈ [infinity] ).

Answer 1

The function p(x) increases on (-5, 1), decreases on
`(1, \infty)\)`, is concave up on (-5, -2), and concave down on
`(-2, \infty).`

The function p(x) exhibits specific behaviors on different intervals:

1. Increasing Interval: (-5, 1) - On this interval, the function p(x) is increasing, indicating that as x increases, the values of p(x) also increase.

2. Decreasing Interval:
`(1, \infty )` - On this interval, the function p(x) is decreasing, signifying that as x increases, the values of p(x) decrease.

3. Concave Up Interval: (-5, -2) - The function p(x) is concave up on this interval, suggesting that the graph is shaped like a cup, and its rate of increase is increasing.

4. Concave Down Interval:
`\( (-2, \infty) \)` - On this interval, p(x) is concave down, indicating a graph shaped like an upside-down cup, with a decreasing rate of increase.

These descriptions provide insights into the directional trends and curvature of the function p(x) across different intervals.