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Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f continuous on the closed interval [-4, 4]? Yes No

Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f continuous on the closed interval [-4, 4]? Yes No

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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Consider the following function and closed interval. f(x) = x3 – 4x2 16x + 5, [-4, 4] Is f continuous on the closed interval [-4, 4]? Yes No If f is differentiable on the open interval (-4, 4), find f'(x). (If it is not differentiable on the open interval, enter DNE.) f'(x) = Find f(-4) and f(4). (If an answer does not exist, enter DNE.) f(-4) %D f(4) = Determine whether Rolle's theorem can be applied to f on the closed interval [-4, 4]. (Select all that apply.) Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed interval[-4, 4]. No, because f is not differentiable on the open interval (-4, 4). No, because f(-4) # f(4). If Rolle's theorem can be applied, find all values of c in the open interval (-4, 4) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's theorem cannot be applied, enter NA.) C = O O O O
Transcribed Image Text:Consider the following function and closed interval. f(x) = x3 – 4x2 16x + 5, [-4, 4] Is f continuous on the closed interval [-4, 4]? Yes No If f is differentiable on the open interval (-4, 4), find f'(x). (If it is not differentiable on the open interval, enter DNE.) f'(x) = Find f(-4) and f(4). (If an answer does not exist, enter DNE.) f(-4) %D f(4) = Determine whether Rolle's theorem can be applied to f on the closed interval [-4, 4]. (Select all that apply.) Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed interval[-4, 4]. No, because f is not differentiable on the open interval (-4, 4). No, because f(-4) # f(4). If Rolle's theorem can be applied, find all values of c in the open interval (-4, 4) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's theorem cannot be applied, enter NA.) C = O O O O
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