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 • 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.
Examples: • Average Speed. • Slope of a secant line.
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.
Examples • Instantaneous Velocity • Slope of the tangent line.
Examples • Example 3 (page 170) • Example 4 (page 171)