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08a.concavity

# 08a.concavity - MAC 2233/001-006 Business Calculus Fall...

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Unformatted text preview: MAC 2233/001-006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Name: Two points . Professor : Stephen Suen Section: Peer Leaders : Hana Aboul-Hosn, Toni Jung, Renan Mendonca 8. Concavity and points of diminishing returns . For a differentiable function f , we say that f is con- cave up on an interval I if f ′ is increasing on the interval, and f is concave down on an interval I if f ′ is decreasing on the interval. Concavity of functions is related to points of diminishing returns. We did not go through points of diminishing returns in class, and the purpose of this worksheet is to discuss this topic in details. Example . (Point of diminishing returns.) Company XYZ wants to investigate the effect of advertise- ment on the revenue of a certain product. The following function is used to model the situation: R =- 1 10 x 3 + 2 x 2 + 4 x + 60 , ≤ x ≤ 14 . where R is the monthly revenue in thousands of dollars, and x is the amount of advertising in thousand dollars each month. The graph ofdollars each month....
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08a.concavity - MAC 2233/001-006 Business Calculus Fall...

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