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Use the limit definition of the derivative to find the instantaneous rate of change c f(x) = 4x + 7x +7 at r 1

Use the limit definition of the derivative to find the instantaneous rate of change c f(x) = 4x + 7x +7 at r 1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 4x +7x +7 at z 1
Transcribed Image Text:Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 4x +7x +7 at z 1
Expert Solution
Step 1

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.

f\left(x\right)=4x^2+7x+7

substitute x+h for x

f\left(x+h\right)=4\left(x+h\right)^2+7\left(x+h\right)+7

f\left(x+h\right)=4\left(x^2+2xh+h^2\right)+7\left(x+h\right)+7

f\left(x+h\right)=4x^2+8xh+4h^2+7x+7h+7

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