2.3a.notes - MAC 2233/001-006 Business Calculus, Fall 2011...

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Unformatted text preview: MAC 2233/001-006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Assistants : Matthew Fleeman, Arbin Rai, Tadesse Zerihun, Vindya Kumari, Junyi Tu, Jing- han Meng An example on estimating derivatives/rates of change from a graph The following graph shows the revenue R (in thousands of dollars per week) of your new convenience store t weeks after it is open. R 10 t A B C D 10 20 30 8 6 4 2 (a) At which of the points A,B,C,D , is the weekly revenue increasing fastest? Give a brief explanation. Solution. A , as the tangent line at A has the biggest slope. (b) For which value(s) of t is revenue flat, that is, neither increasing nor decreasing? Give a brief explanation. Solution. The weekly revenue looks flat when t = 2 , 4 . 5 and perhaps 10, as the tangent lines at these points are horizontal and therefore the instantaneous rate of change is 0. (c) Estimate the slope of the tangent line at the point where t = 9. What does your answer tell you about the revenues of your new store?tell you about the revenues of your new store?...
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