Find f(a), f(a+h), and the difference quotient (f(a+h)-f(a))/(h), where h ≠0. f(x)=(x)/(x+1)

Name: Problem 47, Chapter 2: College Algebra
Uploaded: 2020-06-01T18:42:32-08:00
Duration: 2 min 39 s
Channel: James Kiss
Description: Find f(a), f(a+h), and the difference quotient (f(a+h)-f(a))/(h), where h ≠0. f(x)=(x)/(x+1)

step 1 Given the function, F, we want to find F of A to begin with. You find F of A by plugging A in fo

Find f(a), f(a+h), and the difference quotient...

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Key Concepts

Function Evaluation

This concept involves substituting specific values into a given function. It is the process of determining the output of the function for a particular input. Evaluating f(a) means replacing the variable with a, and likewise, evaluating f(a+h) means replacing the variable with a+h, which is fundamental in understanding how functions behave at different points.

Difference Quotient

The difference quotient is a key concept in calculus used to find the average rate of change of a function over an interval. It is given by the formula [f(a+h) - f(a)]/h where h is a non-zero increment. This expression is the precursor to the derivative, which is obtained by taking the limit as h approaches zero.

Algebraic Simplification of Rational Expressions

When dealing with functions that are ratios of polynomials, it is important to apply techniques of algebraic manipulation to simplify expressions. This includes finding common denominators, combining like terms, and reducing fractions, which are essential skills for handling difference quotients and many other calculus problems.

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