2.5_Solving_Problems_Involving_Rates_of_Change

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2.5 Solving Problems Involving Rates of Change.notebook 1 September 22, 2009 2.5 Solving Problems Involving Rates of Change Recall: Instantaneous rate of change = slope of tangent Tangent Line: a line which only touches the curve at one point Example #1: Consider the graph of the function shown. (a) Determine whether the instantaneous rate of change is positive or negative at each of the indicated points. (b) Estimate the instantaneous rate of change at: (i) x = -3 (ii) x = 2 (c) What type of points exist at x = -3 and at x = 2? What do you remember about intervals of increase and decrease? The instantaneous rate of change is zero at both the maximum and the minimum point. What type of tangent is drawn at a maximum or minimum point? As a curve increases, the slopes of the tangents to the curve are on this interval. As a curve decreases, the slopes of the tangents to the curve are
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Unformatted text preview: on this interval. At a maximum point, the slopes of the tangents must change from to . At a minimum point, the slopes of the tangents must change from to . 2.5 Solving Problems Involving Rates of Change.notebook 2 September 22, 2009 Example #2: For the function f(x) = x 3- 27 x + 1, verify that the point (-3, 55) is either a maximum or a minimum. Example #3: A football is kicked into the air such that its height, h , in metres, after t seconds can be modeled by the function: h(t) = -4.9 t 2 + 26.95 t + 152. (a) Find the time when the football reaches its maximum height. (b) Use the slopes of the tangents to verify that this point is a maximum. Assigned Work: page 112 #3, 4, 5ac, 6ce, 7, 9, 10, 11...
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