The revenue (in thousand of dollars) on spending x thousand dollars of advertisement is given by the following function : 1 R(x) = (150x? – x*); 0< x < 100 1500 a) Find the local extrema of R, if any b) Determine the interval when is R increasing & decreasing. c) Identify the point of diminishing returns.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter5: Graphs And The Derivative
Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test
Problem 19E
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The revenue (in thousand of dollars) on spending x thousand dollars of
advertisement is given by the following function :
R(x) =
(150x² – x³); 0 <x< 100
- X
1500
a) Find the local extrema of R, if any
b) Determine the interval when is R increasing & decreasing.
c) Identify the point of diminishing returns.
d) Determine the interval when is R concave up & concave down.
e) Sketch the graph.
f) What is the maximum revenue?
Transcribed Image Text:The revenue (in thousand of dollars) on spending x thousand dollars of advertisement is given by the following function : R(x) = (150x² – x³); 0 <x< 100 - X 1500 a) Find the local extrema of R, if any b) Determine the interval when is R increasing & decreasing. c) Identify the point of diminishing returns. d) Determine the interval when is R concave up & concave down. e) Sketch the graph. f) What is the maximum revenue?
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