   Chapter 10.6, 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 29-38, compute the indicated derivative. q ( p ) = 1 0.5 p − 3.1 ; q ′ ( 2 )

To determine

To calculate: The value of the derivative q(2) for the function q(p)=10.5p3.1.

Explanation

Given Information:

The provided function is q(p)=10.5p3.1.

Formula used:

The difference quotient formula is used which is as follows:

f(a)=limh0f(a+h)f(a)h

Calculation:

Consider the function, q(p)=10.5p3.1

The difference quotient formula used to estimate the exact value of derivative algebraically is:

f(a)=limh0f(a+h)f(a)h

But, according to the question,

q(a)=limh0q(a+h)q(a)h

Substitute a=2 into the above formula,

q(2)=limh0q(2+h)q(2)h

Here q(2)=10.5(2)3.1 then,

q(2+h)=10.5(2+h)3.1

Substitute the values of q(2) and q(2+h) in the function q(2)=limh0q(2+h)q(2)h as,

q(2)=limh0[10.5(2+h)3

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