   Chapter 10.5, Problem 42E 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 41-48, estimate the indicated derivative by any method. [HINT: See Example 2.] s ( t ) = 1 t 3 ;  estimate  s ' ( − 2 )

To determine

To calculate: The value of s(2) from the function s(x)=1t3.

Explanation

Given Information:

The provided function is s(x)=1t3.

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 s(x)=1t3.

Now, apply the balanced difference quotient formula and substitute the value a=2 and h=0.0001:

s(2)=s(2+0.0001)s(20.0001)2(0.0001)

Calculate s(2+0.0001) by substituting 2+0.0001 in the function s(x)=1t3:

s(2+0.0001)=1(2+0.0001)3=1(1

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