   Chapter 10.6, Problem 7E 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 ) = 2 x − x 2 ; a = − 1

To determine

To calculate: The value of f(a) algebraically when a=1 for the function f(x)=2xx2.

Explanation

Given Information:

The provided function is f(x)=2xx2 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:

(ab)2=a2+b22ab

Calculation:

Consider the provided function,

f(x)=2xx2

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 f(x),

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

Simplify (

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