Question

score on last try: 0 of 2 pts. see details for more. at least one scored part is incorrect. jump to first changable incorrect part. you can retry this question below the function graphed above has: positive derivative on the open interval(s) negative derivative on the open interval(s) if an answer contains more than one interval, write your answer as a union of intervals. add work

Explanation:

Step1: Recall derivative - slope relationship

The derivative of a function represents the slope of the tangent line. A positive - slope means a positive derivative and a negative - slope means a negative derivative.

Step2: Identify positive - slope intervals

Looking at the graph, the function is increasing (has a positive slope) on the interval where the curve goes up from left to right. From the graph, the function is increasing on the open interval \((-2,1)\).

Step3: Identify negative - slope intervals

The function is decreasing (has a negative slope) on the intervals where the curve goes down from left to right. From the graph, the function is decreasing on the open intervals \((-\infty,-2)\cup(1,\infty)\).

Answer:

Positive derivative on the open interval(s): \((-2,1)\)
Negative derivative on the open interval(s): \((-\infty,-2)\cup(1,\infty)\)