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03a.rates - MAC 2233/001-006 Business Calculus Fall 2011...

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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 3. Rates of change and derivatives We encounter rates of change in our everyday life. For example, speed is the rate of change of distance over time. We shall try to find rates of change graphically and algebraically in this handout. Example . (Rates of change, graphically) The monthly revenue R (in thousands of dollars) of a bakery store t months after its opening is displayed in the chart below. (a) Estimate the average rate of change of R from t = 0 to t = 3. Solution. We find from the graph that R = 0 when t = 0, and that R = 4 . 5 when t = 3. Thus average rate of change of R from t = 0 to t = 3 equals Δ R Δ t = 4 . 5 - 0 3 - 0 = 0 . 5 thousand dollars per month . This shows that the revenue of the store is increasing on average at a rate of 500 dollars per month during the period between t = 0 and t = 3. We note that this average rate of change equals the slope of the secant line from t
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