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Lesson 3.7

Lesson 3.7. Rates of Change. Average Rate of Change. Change in f(x) = f(b) – f(a) Change in x b - a. Example. A balloon is being filled with water. Its approximate volume in gallons is v(x) = x 3

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Lesson 3.7

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  1. Lesson 3.7 Rates of Change

  2. Average Rate of Change Change in f(x) = f(b) – f(a) Change in x b - a

  3. Example • A balloon is being filled with water. Its approximate volume in gallons is v(x) = x3 55 where x is the radius of the balloon in inches. Find the average rate of change of the volume of the balloon as the radius increases from 5 to 10.

  4. Yet another example • A small manufacturing company makes specialty office desks. The cost (in thousands of dollars) of producing x desks is given by the function c(x) = 0.0009x3 - 0.06x2 + 1.6x + 5 Find the average rate of change for: • 0- 10 desks • 10-30 desks • 30-50 desks

  5. Geometric Interpretation of Average Rate of Change • The average rate of change of f from x = a to x = b  f(b) – f(a) = slope of the secant line b – a joining (a, f(a)) and (b, f(b)) on the graph of f.

  6. Don’t get bent out of shape…but do you remember this?

  7. If yes…lets turn to page 220 If no…turn to page 220 anyway • Use the difference quotient to find the average rate of change of V as x changes from 8 to 8.01. • By the way

  8. That is all kiddos…by the way here is Emma from Halloween 2010!

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