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2.5 Solving Problems involving Rates of change

This study explores the average rate of change in height for an aircraft simulating weightlessness and a ball on a water wheel across specified time intervals. It involves calculating average rates, estimating instantaneous rates at critical points, and drawing conclusions regarding slopes at maxima and minima. We analyze the behavior of tangent lines and sketch graphs to visually interpret the motion dynamics. Homework exercises deepen understanding of rates of change through hands-on application.

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2.5 Solving Problems involving Rates of change

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  1. 2.5 Solving Problems involving Rates of change Thursday September 27, 2012

  2. 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

  3. 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?

  4. 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

  5. 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.

  6. 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?

  7. Homework: Page 111 #1 -#11

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