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4.4_Polynomial_ROC_Lesson

4.4_Polynomial_ROC_Lesson - Lesson_PolynomialROC.notebook...

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Unformatted text preview: Lesson_PolynomialROC.notebook October 15, 2009 4.4 Rates of Change in Polynomial Functions (1) Average Rate of Change The average rate of change represents the slope of the secant over the interval Average Rate of Change (2) Instantaneous Rate of Change The instantaneous rate of change represents the slope of the tangent to the curve at the point x = a. To determine the instantaneous rate of change at a point, we need to choose really small intervals on either side of x = a. Instantaneous Rate of Change (use ) 1 Lesson_PolynomialROC.notebook October 15, 2009 Example #1: Consider the graph of the function shown. (a) Determine an interval where the average rate of change is: (i) positive (ii) negative (iii) zero (b) Determine a point where the instantaneous rate of change is: (i) positive (ii) negative (iii) zero (c) Calculate the average rate of change for Example #2: Consider the function f(x) = 3x2 + 2x ­ 1. (a) Calculate the average rate of change on the interval (b) Estimate the instantaneous rate of change at x = ­2. 2 Lesson_PolynomialROC.notebook October 15, 2009 (c) What is the sign of the instantaneous rate of change at x = ­2? Does this make sense? (d) Find the equation of the tangent line to the curve at x = ­ 2? Example #3: The population of a city has been tracked since 1980. The population growth, P(x), is a function of the number of years, x, since 1980. (a) At what rate is the population growing between 1995 and 2010? 3 Lesson_PolynomialROC.notebook October 15, 2009 Example #3: (continued) (b) At what rate is the population expected to grow in 2012? Assigned Work: page 235 #1 ­ 4, 5bce, 6bce, 7, 9, 10 (include sketches for 9 & 10) Chapter 4 Review Questions: page 240 #1ad, 3 ­ 5, 6bd, 7bc, 8cd, 9, 10a, 11, 14c, 15 ­ 17 4 ...
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