A manufacturer sells video games with the following cost and revenue functions (

Question

A manufacturer sells video games with the following cost and revenue functions (in dollars), where x is the number of games sold Determine the interval(s) on which the profit function is increasing c(x) = 0.17x2 -0.0001x3 R(x) = 0.710x2 - 0.0002x3 The profit function is increasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed. Type N if the function is never increasing.)

Explanation / Answer

Profit = Revenue - Cost = .54x^2 - .0001x^3 Find when derivative of profit is zero P ' = 1.08x - .0003x^2 P ' = 0 ------> 1.08x - .0003x^2 = 0 -----> .0003x(3600 - x) = 0 ----> x = 0 or x = 3600 Pick test values on each side of critical values (note x cannot be negative since it is representing a production level) P ' (1) is positive P ' (3700) is negative Therefore profit is increasing on the interval (0, 3600)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.