Question

the graph of a companys marginal profit p(t) at month t is shown over the interval 0, 56.
a. on what open interval(s) is the profit p(t) increasing?
b. on what open interval(s) is the profit p(t) decreasing?
a. list the interval(s) on which p(t) is increasing. (type your answer in interval notation. use a comma to separate answers as needed.)

Explanation:

Step1: Recall the relationship between \(P(t)\) and \(P^{\prime}(t)\)

If \(P^{\prime}(t)>0\), then \(P(t)\) is increasing.

Step2: Analyze the graph of \(P^{\prime}(t)\)

Looking at the graph, \(P^{\prime}(t)>0\) on the intervals \((0,14)\) and \((28,42)\)

Answer:

\((0,14),(28,42)\)