   Chapter 10.6, Problem 21E 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 ) = 2 x − x 2

To determine

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

Explanation

Given Information:

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

Formula used:

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

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

The square of sum formula,

(a+b)2=a2+b2+2ab

Calculation:

Consider the function, f(x)=2xx2

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)=2xx2 then,

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

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[2(

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