   Chapter 1.4, Problem 33E

Chapter
Section
Textbook Problem

Evaluating a Function In Exercises 29-34, evaluate the difference quotient and simplify the result. See Example 4. f ( x ) = 1 x − 2 f ( x + Δ x ) − f ( x ) Δ x

To determine

To calculate: The value of the expression f(x+Δx)f(x)Δx if the function is f(x)=1x2.

Explanation

Given information:

The provided expression is f(x+Δx)f(x)Δx and the function is f(x)=1x2.

Formula used:

The distributive property for any numbers a, b and c is a(b+c)=ab+ac.

Calculation:

Consider the function, f(x)=1x2

Substitute (x+Δx) for x in the function f(x)=1x2.

f(x+Δx)=1x+Δx2

Consider the expression, f(x+Δx)f(x)Δx

Substitute f(x+Δx)=1x+Δx2 and f(x)=1x2 in the expression f(x+Δx)f(x)Δx

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