Finding the Difference Quotient of a Function (3.18.5)

Question 1

• Difference quotient:

D(x) = (f(x+h)-f(x))/h

Answer 1

• Difference quotient:

D(x) = (f(x+h)-f(x))/h

Question 2

This example shows how the difference quotient formula is used to solve problems. You are given the function (3x – 5). In the formula, replace f (x + h) with 3(x + h) – 5. Replace –f (x) with –(3x – 5). Remember: In the second substitution all the signs will change because you are subtracting. Then remove your parentheses, combine like terms, and you have your answer. Note: Your answer MUST presume that h is not equal to 0. In this example you are given the function f (x) = 1 – x^2 and are asked to find the difference quotient. Substitute (x + h) for x. Remove parentheses with a careful regard for signs. Combine like terms and reduce where possible to find your answer. In this case, the difference quotient for the function f (x) = 1 – x^2 is –2x – h. Assume as a requirement that h cannot equal 0.

Answer 2

This example shows how the difference quotient formula is used to solve problems. You are given the function (3x – 5). In the formula, replace f (x + h) with 3(x + h) – 5. Replace –f (x) with –(3x – 5). Remember: In the second substitution all the signs will change because you are subtracting. Then remove your parentheses, combine like terms, and you have your answer. Note: Your answer MUST presume that h is not equal to 0. In this example you are given the function f (x) = 1 – x^2 and are asked to find the difference quotient. Substitute (x + h) for x. Remove parentheses with a careful regard for signs. Combine like terms and reduce where possible to find your answer. In this case, the difference quotient for the function f (x) = 1 – x^2 is –2x – h. Assume as a requirement that h cannot equal 0.