Assuming the limit exists, the definition of the derivative If h > 0, then this approximation is

Assuming the limit exists, the definition of the derivative

implies that if h is small, then an approximation to f'(a) is given by

If h > 0, then this approximation is called a forward difference quotient; if h < 0, it is a backward difference quotient. As shown in the following exercises, these formulas are used to approximate f' at a point when f is a complicated function or when f is represented by a set of data points.

The following table gives the distance f(t) fallen by a smoke jumper t seconds after she opens her chute.

a. Use the forward difference quotient with h = 0.5 to estimate the velocity of the smoke jumper at t = 2 seconds.

b. Repeat part (a) using the centered difference quotient.

Transcribed Image Text:

f(a + h) – f(a) f"(a) lim h. f(a + h) – f(a) f"(a)