   Chapter 10.6, Problem 23E 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 15-28, compute the derivative function f ′ ( x ) algebraically. (Notice that the functions are the same as those in Exercises 1-14,) [HINT: See Example 2 and 3.] f ( x ) = x 3 + 2 x

To determine

To calculate: The value of f(x) algebraically for the function f(x)=x3+2x.

Explanation

Given Information:

The provided function is f(x)=x3+2x.

Formula used:

The quotient formula is used which can be represented as follows:

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

The expansion of (a+b)3 is done as follows:

(a+b)3=a3+3a2b+3ab2+b3

Calculation:

Consider the function, f(x)=x3+2x

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

f(x)=limh0f(x+h)f(x)h.

Here f(x)=x3+2x

Then,

f(x+h)=(x+h)3+2(x+h)

Substitute the values of f(x) and f(x+h) in the formula f(x)=limh0f(x+h)f(x)h as,

f(x)=limh0[(x+h)3+2(

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