f(x) = 2x – 9x² – 24x + 10 on the interval [-6, 10]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (-6, 10) such tha f'(c) is equal to this mean slope. For this problem, there are two values of c that work. The smaller one is and the larger one is
f(x) = 2x – 9x² – 24x + 10 on the interval [-6, 10]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (-6, 10) such tha f'(c) is equal to this mean slope. For this problem, there are two values of c that work. The smaller one is and the larger one is
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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![**Function and Interval:**
\[ f(x) = 2x^3 - 9x^2 - 24x + 10 \] on the interval \([-6, 10]\).
**Task:**
Find the average or mean slope of the function on this interval.
**Mean Value Theorem Application:**
By the Mean Value Theorem, we know there exists a \( c \) in the open interval \((-6, 10)\) such that \( f'(c) \) is equal to this mean slope.
**Solution:**
For this problem, there are two values of \( c \) that work. The smaller one is \(\_\_\_\_\_\_\_\_\_\) and the larger one is \(\_\_\_\_\_\_\_\_\_\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f1c68a1-c113-41cc-b0cf-42f2666e5687%2Fc6b5fbe9-de13-4898-ac6a-e51531d23798%2Fk3o3j08_processed.png&w=3840&q=75)
Transcribed Image Text:**Function and Interval:**
\[ f(x) = 2x^3 - 9x^2 - 24x + 10 \] on the interval \([-6, 10]\).
**Task:**
Find the average or mean slope of the function on this interval.
**Mean Value Theorem Application:**
By the Mean Value Theorem, we know there exists a \( c \) in the open interval \((-6, 10)\) such that \( f'(c) \) is equal to this mean slope.
**Solution:**
For this problem, there are two values of \( c \) that work. The smaller one is \(\_\_\_\_\_\_\_\_\_\) and the larger one is \(\_\_\_\_\_\_\_\_\_\).
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