MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A technology start-up’s revenue, in thousands of dollars, t months after launch is modeled by a differentiable function R with R(0)=0. The marginal revenue is given by
R′(t)=60e−0.1t(1−0.02t),t≥0.
Respond to each part, including appropriate justification.
(a) Determine the open intervals on which the revenue is increasing. Show how you used the given model to reach your conclusion.
(b) Determine the open intervals on which the revenue is concave down. Support your answer analytically.
(c) Identify the open interval(s) on which the revenue is increasing at a decreasing rate. Explain your reasoning in terms of R′ and R′′.
(d) At what time does the revenue grow at its fastest rate? Justify your answer and state the corresponding marginal revenue (in thousands of dollars per month) at that time.