Section 3'3: Rates of Change

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Section 3.3 Rates of Change

• HWK 1-15, 27,29, pp. 173-175.

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We will be dealing with two main concepts

• Average Rate of Change
• Instantaneous Rate of Change

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Average rate of change

• Given a function y f(x) and two values of x
  (say, a and b), the average rate of change is the
  quotient (f(b) f(a))/b-a
• That quantity is also sometimes called the
  difference quotient.

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Examples

• Average Speed.
• Slope of a secant line.

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Instantaneous Rate of Change

• The instantaneous rate of change at x a is the
  expected value of the difference quotient (f(ah)
  f(a))/h as h goes to zero.

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Examples

• Instantaneous Velocity
• Slope of the tangent line.

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Examples

• Example 3 (page 170)
• Example 4 (page 171)