   Chapter 10.5, Problem 38E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 37–40, use a quick approximation to estimate the derivative of the given function at the indicated point. [HINT: See Example 2(a).] f ( x ) = x 3 − 1 ; x = − 3

To determine

To calculate: The derivative of the function f(x)=x31 at the point x=3 by use of quick approximation.

Explanation

Given Information:

The function is f(x)=x31 and the point is x=3.

Formula used:

The balanced difference quotient:

When f is differentiable at a, the approximate value of f(a) can be calculated as,

f(a)=f(a+h)f(ah)2h

Where, the value of h=0.0001

Calculation:

Consider the function f(x)=x31 and the point is x=3.

Now, apply the balanced difference quotient formula and substitute the value a=3 and h=0.0001:

f(3)=f(3+0.0001)f(30.0001)2(0.0001)

Calculate f(3+0.0001) by substituting 3+0.0001 in the function f(x)=x31:

f(3+0

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