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2.5 Solving Problems involving Rates of change. Thursday September 27, 2012. Problem #1:. The flight of an aircraft used to stimuylate weightlessness is modelled by :.
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2.5 Solving Problems involving Rates of change Thursday September 27, 2012
Problem #1: • The flight of an aircraft used to stimuylate weightlessness is modelled by : • Determine the average rate of change in height for each of the following intervals and interpret the meaning of your calculations: • 0 – 30 sec ii) 0-15 sec iii) 15-30 sec • Use your results to estimate the instantaneous rate of change at 15 seconds
Sketch a graph of this function. When does the maximum height occur? • What is the Iroc at the maximum point? e) What would the tangent line look like at the maximum point?
Conclusions: • The tangent line at a maximum or minimum point are ____________. Thus, their slope is ________. • So the Iroc at Max or Min Points must be _______. • Tangent lines before a max. value have a ______ slope and a _________ slope after the max. value. • Tangent lines before a min. value have a _________ slope and a _______ slope after the min. value
Problem 2: A ball is stuck on a water wheel. Its height (h) with respect to time (t) is given by: Will the ball be at its lowest point at 70 seconds? Use Aroc to predict Aroc (60 -70 seconds) Aroc (70 – 80 seconds) Sketch a graph of the function to verify your results.
Problem 3: Estimate the Iroc using the difference quoient when x = -2 for Based on the Iroc, what conclusion can be made about a local maxima or minima?
Homework: Page 111 #1 -#11
