Explanation The SDQ is the average rate of change of the function in the interval ( x − h , x + h ) Given: Consider f ( x ) is a quadratic polynomial represented as: f ( x ) = p x 2 + q x + r ... ( 1 ) Formula Used: The derivative of f at x = a by using the SDQ method is: f ' ( a ) = lim h → 0 f ( a + h ) − f ( a − h ) 2 h Calculation: Applying the SDQ method f ' ( a ) is determined as: f ' ( a ) = lim h → 0 f ( a + h ) − f ( a − h ) 2 h = lim h → 0 p ( a + h ) 2 + q ( a + h ) + r − p ( a − h ) 2 − q ( a − h ) − r 2 h = lim h → 0 p ( a 2 + h 2 + 2 a h ) + q a + q h + r − p ( a 2 + h 2 − 2 a h ) − q a + q h − r 2 h = lim h → 0 p a 2 + p

Loose-leaf Version for Calculus: Early Transcendentals Combo 3e & WebAssign for Calculus: Early Transcendentals 3e (Life of Edition)

3rd Edition

ISBN: 9781319019846

Author: Jon Rogawski, Colin Adams

Publisher: W. H. Freeman

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Question

Chapter 3.1, Problem 77E

To determine

We need to prove that if $f$ is a quadratic polynomial, then the SDQ at $x = a$ (for any $h \neq 0$ ) is $f^{'} (a)$ and we need to explain the graphical meaning of this.

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Chapter 3.1, Problem 76E

Chapter 3.1, Problem 78E

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Chapter 3 Solutions

Loose-leaf Version for Calculus: Early Transcendentals Combo 3e & WebAssign for Calculus: Early Transcendentals 3e (Life of Edition)

Ch. 3.1 - Prob. 1PQ Ch. 3.1 - Prob. 2PQ Ch. 3.1 - Prob. 3PQ Ch. 3.1 - Prob. 4PQ Ch. 3.1 - Prob. 5PQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E

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Prob. 43CRE Ch. 3 - Prob. 44CRE Ch. 3 - Prob. 45CRE Ch. 3 - Prob. 46CRE Ch. 3 - Prob. 47CRE Ch. 3 - Prob. 48CRE Ch. 3 - Prob. 49CRE Ch. 3 - Prob. 50CRE Ch. 3 - Prob. 51CRE Ch. 3 - Prob. 52CRE Ch. 3 - Prob. 53CRE Ch. 3 - Prob. 54CRE Ch. 3 - Prob. 55CRE Ch. 3 - Prob. 56CRE Ch. 3 - Prob. 57CRE Ch. 3 - Prob. 58CRE Ch. 3 - Prob. 59CRE Ch. 3 - Prob. 60CRE Ch. 3 - Prob. 61CRE Ch. 3 - Prob. 62CRE Ch. 3 - Prob. 63CRE Ch. 3 - Prob. 64CRE Ch. 3 - Prob. 65CRE Ch. 3 - Prob. 66CRE Ch. 3 - Prob. 67CRE Ch. 3 - Prob. 68CRE Ch. 3 - Prob. 69CRE Ch. 3 - Prob. 70CRE Ch. 3 - Prob. 71CRE Ch. 3 - Prob. 72CRE Ch. 3 - Prob. 73CRE Ch. 3 - Prob. 74CRE Ch. 3 - Prob. 75CRE Ch. 3 - Prob. 76CRE Ch. 3 - Prob. 77CRE Ch. 3 - Prob. 78CRE Ch. 3 - Prob. 79CRE Ch. 3 - Prob. 80CRE Ch. 3 - Prob. 81CRE Ch. 3 - Prob. 82CRE Ch. 3 - Prob. 83CRE Ch. 3 - Prob. 84CRE Ch. 3 - Prob. 85CRE Ch. 3 - Prob. 86CRE Ch. 3 - Prob. 87CRE Ch. 3 - Prob. 88CRE Ch. 3 - Prob. 89CRE Ch. 3 - Prob. 90CRE Ch. 3 - Prob. 91CRE Ch. 3 - Prob. 92CRE Ch. 3 - 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We need to prove that if f is a quadratic polynomial, then the SDQ at x = a (for any h ≠ 0 ) is f ' ( a ) and we need to explain the graphical meaning of this.

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We need to prove that if fis a quadratic polynomial, then the SDQ at x=a(for any h≠0) is f'(a)and we need to explain the graphical meaning of this.

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We need to prove that if $f$ is a quadratic polynomial, then the SDQ at $x = a$ (for any $h \neq 0$ ) is $f^{'} (a)$ and we need to explain the graphical meaning of this.