- Consider the function f(x) = 2x² - 16x 5 on the interval [2, 6]. Find the value(s) for c that satisfy Rolle's Theorem in the open interval (2, 6).
- Consider the function f(x) = 2x² - 16x 5 on the interval [2, 6]. Find the value(s) for c that satisfy Rolle's Theorem in the open interval (2, 6).
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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![**Problem Statement:**
Consider the function \( f(x) = 2x^2 - 16x - 5 \) on the interval \([2, 6]\). Find the value(s) for \( c \) that satisfy Rolle's Theorem in the open interval \( (2, 6) \).
**Guidance:**
To solve this problem according to Rolle's Theorem, ensure that the function:
1. Is continuous on the closed interval \([2, 6]\).
2. Is differentiable on the open interval \((2, 6)\).
3. Satisfies \( f(2) = f(6) \).
Once these conditions are met, then there exists at least one value \( c \) in the open interval \((2, 6)\) such that \( f'(c) = 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03532cdf-3ae3-42ec-b6da-b6f111ab5ca1%2F5f1ad6a6-f7ca-48d3-b7e1-e8fc8f174c92%2Fz56ptt9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Consider the function \( f(x) = 2x^2 - 16x - 5 \) on the interval \([2, 6]\). Find the value(s) for \( c \) that satisfy Rolle's Theorem in the open interval \( (2, 6) \).
**Guidance:**
To solve this problem according to Rolle's Theorem, ensure that the function:
1. Is continuous on the closed interval \([2, 6]\).
2. Is differentiable on the open interval \((2, 6)\).
3. Satisfies \( f(2) = f(6) \).
Once these conditions are met, then there exists at least one value \( c \) in the open interval \((2, 6)\) such that \( f'(c) = 0 \).
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