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Section 3.3: Rates of Change

Section 3.3: Rates of Change. HWK: 1-15, 27,29, pp. 173-175. We will be dealing with two main concepts:. Average Rate of Change Instantaneous Rate of Change. Average rate of change.

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Section 3.3: Rates of Change

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  1. Section 3.3: Rates of Change • HWK: 1-15, 27,29, pp. 173-175.

  2. We will be dealing with two main concepts: • Average Rate of Change • Instantaneous Rate of Change

  3. 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.

  4. Examples: • Average Speed. • Slope of a secant line.

  5. Instantaneous Rate of Change • The instantaneous rate of change at x = a is the expected value of the difference quotient (f(a+h) – f(a))/h as h goes to zero.

  6. Examples • Instantaneous Velocity • Slope of the tangent line.

  7. Examples • Example 3 (page 170) • Example 4 (page 171)

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