   Chapter 10.6, Problem 10E 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 1-14, compute f ′ ( a ) algebraically for the given value of a. [HINT: See Example 1.] f ( x ) = x − 2 x 3 ; a = 1

To determine

To calculate: The value of f(a) algebraically when a=1 for the function f(x)=x2x3.

Explanation

Given Information:

The provided function is f(x)=x2x3 and the derivative of f is to be calculated at a=1.

Formula used:

The definition of derivative in terms of the difference quotient:

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

The algebraic identity:

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

Calculation:

Consider the provided function,

f(x)=x2x3

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

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

Substitute a=1 in the above formula,

f(1)=limh0f(1+h)f(1)h

Substitute the values of f(1) and f(1+h) in the above expression,

f(1)=limh0f(1+h)f(1)h=limh0[(1+h)2(1+h)3][12(1)3]h

Simplify (1+h)3 using algebraic identity,

f(1)=limh0[(1+h)2(1+h)3][12(1)3]h

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