Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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![**Title: Applying the Mean Value Theorem to Quadratic Functions**
**Course Information:**
- 2021 Fall CRN 45556 Math 2413-10 Remote 10-1140
**Homework Assignment: 4.2**
- Question 4, Part 1 of 4
- HW Score: 83.33%, 5 of 6 points
- Points: 0 of 1
**Student Name:**
- Zeltzin Soriano
- Date: 10/29/21 2:00 PM
**Problem Description:**
Consider the quadratic function \( f(x) = Ax^2 + Bx + C \), where \( A \), \( B \), and \( C \) are real numbers, and \( A \neq 0 \). Show that when the Mean Value Theorem is applied to \( f \) on the interval \([a, b]\), the number \( c \) guaranteed by the theorem is the midpoint of the interval.
**Instructions:**
Apply the Mean Value Theorem to \( f(x) \) on \([a, b]\). First, find
\[
\frac{f(b) - f(a)}{b-a}
\]
**Solution Space:**
A box is provided to enter the solution for
\[
\frac{f(b) - f(a)}{b-a}
\]
Complete this problem using the definition of the Mean Value Theorem and demonstrate the result that the value of \( c \) is the midpoint of \([a, b]\).](https://content.bartleby.com/qna-images/question/ef8a5e1f-063c-447b-b313-4700820505e4/1e961049-efff-44c1-ac58-83d3ebd46346/ho1nh2d_processed.jpeg)
Transcribed Image Text:**Title: Applying the Mean Value Theorem to Quadratic Functions**
**Course Information:**
- 2021 Fall CRN 45556 Math 2413-10 Remote 10-1140
**Homework Assignment: 4.2**
- Question 4, Part 1 of 4
- HW Score: 83.33%, 5 of 6 points
- Points: 0 of 1
**Student Name:**
- Zeltzin Soriano
- Date: 10/29/21 2:00 PM
**Problem Description:**
Consider the quadratic function \( f(x) = Ax^2 + Bx + C \), where \( A \), \( B \), and \( C \) are real numbers, and \( A \neq 0 \). Show that when the Mean Value Theorem is applied to \( f \) on the interval \([a, b]\), the number \( c \) guaranteed by the theorem is the midpoint of the interval.
**Instructions:**
Apply the Mean Value Theorem to \( f(x) \) on \([a, b]\). First, find
\[
\frac{f(b) - f(a)}{b-a}
\]
**Solution Space:**
A box is provided to enter the solution for
\[
\frac{f(b) - f(a)}{b-a}
\]
Complete this problem using the definition of the Mean Value Theorem and demonstrate the result that the value of \( c \) is the midpoint of \([a, b]\).
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