   Chapter 9.3, Problem 2CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# For the function y = f ( x ) = x 2 − x + 1 , find each of the following.(a) f ( x + h ) − f ( x ) (b) f ( x + h ) − f ( x ) h (c) f ' ( x ) = lim x → 0 f ( x + h ) − f ( x ) h (d) f ' ( 2 )

(a)

To determine

To calculate: The value of f(x+h)f(x), for the function, f(x)=x2x+1.

Explanation

Given Information:

The provided function is f(x)=x2x+1.

Formula used:

The property of square of sum of two terms, a and b,

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

Calculation:

Consider the provided function,

f(x)=x2x+1

For x=x+h, substitute x+h for x,

f(x+h)=(x+h)2(x+h)+1

Substitute (x+h)2(x+h)+1 for f(x+h) and x2x+1 for f(x) in the provided expression,

So,

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

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