Answer:
increasing: (-∞, -5) and (-2, ∞)
decreasing: (-5, -2)
Step-by-step explanation:
You want to know the intervals of increase and decrease for the cubic relation that has a relative maximum at (-5, 8) and a relative minimum at (-2, 5).
Increasing
A function is "increasing" when y values increase as x-values increase. The graph has positive slope, extending upward to the right.
The graph goes up to a relative maximum, so is always increasing on the interval to the left of a relative maximum.
The graph goes up from a relative minimum, so is always increasing to the right of a relative minimum.
A turning point is not included in the "increasing" interval, because the slope is 0 there (not positive).
This graph is increasing on the intervals ...
(-∞, -5) and (-2, ∞)
Decreasing
A function is "decreasing" when y values decrease as x-values increase. The graph has negative slope, extending downward to the right.
The graph goes down to a relative minimum, so is always decreasing to the left of a relative minimum.
The graph goes down from a relative maximum, so is always decreasing on the interval to the right of a relative maximum.
A turning point is not included in the "decreasing" interval, because the slope is 0 there (not negative).
This graph is decreasing on the interval ...
(-5, -2)
