A company estimates that it will sell N(x) units of a product after spending x thousand dollars on advertising, as given by N(x)=−5x^3+200x^2−3800x+16000,10≤x≤40. (A) Use interval notation to indicate when the rate of change of sales N′(x) is increasing. (B) Use interval notation to indicate when the rate of change of sales N′(x) is decreasing. (C) Find the average of the x values of all inflection points of N(x). (D)Find the maximum rate of change of sales.
A company estimates that it will sell N(x) units of a product after spending x thousand dollars on advertising, as given by N(x)=−5x^3+200x^2−3800x+16000,10≤x≤40. (A) Use interval notation to indicate when the rate of change of sales N′(x) is increasing. (B) Use interval notation to indicate when the rate of change of sales N′(x) is decreasing. (C) Find the average of the x values of all inflection points of N(x). (D)Find the maximum rate of change of sales.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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A company estimates that it will sell N(x) units of a product after spending x thousand dollars on advertising, as given by
N(x)=−5x^3+200x^2−3800x+16000,10≤x≤40.
(A) Use interval notation to indicate when the rate of change of sales N′(x) is increasing.
(B) Use interval notation to indicate when the rate of change of sales N′(x) is decreasing.
(C) Find the average of the x values of all inflection points of N(x).
(D)Find the maximum rate of change of sales.
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