Precalculus Class Notes F4 The Difference Quotient
The difference quotient of a function f is an expression of the
form
f ( x + h) − f ( x)
h
where h ≠ 0.
Example:
f ( x ) = x2 − 2x
a. Find f ( x + h )
b. Find the difference quotient of f and simplify the result.
c. Evaluate the difference quotient for x = 3 and h = 0.1. Interpret your results.
d. Evaluate the difference quotient for x = 0 and h = 1. Then
sketch a graph that illustrates the result.
Example:
f ( x ) = 1 − x3
(a) Find f(x +h).
(b) Find the difference quotient of f and simplify the result.
(c) Evaluate the difference quotient for x = –2 and h = 0.1. Interpret your result.
Example 6:
Let the distance d in feet that a racehorse runs in t seconds be d(t) = 2t2 for 0 ≤ t ≤ 10.
(a) Find d(t +h).
(b) Find the difference quotient of d and simplify the result.
(c) Evaluate the difference quotient for t = 7 and h = 0.1. Interpret your results.
(d) Evaluate the difference quotient for t = 4 and h = 1. Interpret your results.