Select the statement that is false about the difference quotient.   The difference quotient can be represented by f(x+h)−f(x)(x+h)−x or f(x+h)−f(x)h The difference quotient is a more general form of the average rate of change of a function on an interval h units long. The difference quotient describes the general behavior of a function over some interval h units long when the rate of change is not constant. As the value of h gets smaller and smaller, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)). As the value of h gets larger and larger, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)).

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Select the statement that is false about the difference quotient.

 

  • The difference quotient can be represented by f(x+h)−f(x)(x+h)−x or f(x+h)−f(x)h
  • The difference quotient is a more general form of the average rate of change of a function on an interval h units long.
  • The difference quotient describes the general behavior of a function over some interval h units long when the rate of change is not constant.
  • As the value of h gets smaller and smaller, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)).
  • As the value of h gets larger and larger, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)).

 

 

 

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