   Chapter 10.5, Problem 39E 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 2 4 − x 3 3 ; x = − 1

To determine

To calculate: The derivative of the function f(x)=x24x33 at the point x=1 by use of quick approximation.

Explanation

Given Information:

The provided function is f(x)=x24x33 and the point is x=1.

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)=x24x33 and the point is x=1.

Now, apply the balanced difference quotient formula and substitute the value a=1 and h=0.0001:

f(1)=f(1+0.0001)f(10.0001)2(0.0001)

Calculate f(1+0.0001) by substituting 1+0.0001 in the function f(x)=x24x33:

f(1+0.0001)=(1+0.0001)24(1+0.0001)33=(0.9999)24(0

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