1) If an odd function h(x) has a local maximum value at x c, can anything be said about h at the value x = - c? Give reasons for your answer. 2) Suppose that g" is continuous on [a, b] and that g has three zeros in the interval. Show that g" has at least one zero in (a, b). Generalize your result. 3) Explain why the following statements are true or false: a) If fis continuous on [2, 5] and differentiable on (2, 5), and f(2) o, then there is a number c between 2 and 5 where f '(c) o and f5) o. = b) Iffis continuous on [2, 5] then there is an absolute maximum and an absolute minimum on [2, 5]. c) Iffis continuous on [2, 5] and differentiable on (2, 5), andf(2) = 6 and f(5) = 15, then there is a number c between 2 and 5 wheref '(c) = 3.
1) If an odd function h(x) has a local maximum value at x c, can anything be said about h at the value x = - c? Give reasons for your answer. 2) Suppose that g" is continuous on [a, b] and that g has three zeros in the interval. Show that g" has at least one zero in (a, b). Generalize your result. 3) Explain why the following statements are true or false: a) If fis continuous on [2, 5] and differentiable on (2, 5), and f(2) o, then there is a number c between 2 and 5 where f '(c) o and f5) o. = b) Iffis continuous on [2, 5] then there is an absolute maximum and an absolute minimum on [2, 5]. c) Iffis continuous on [2, 5] and differentiable on (2, 5), andf(2) = 6 and f(5) = 15, then there is a number c between 2 and 5 wheref '(c) = 3.
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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![1) If an odd function h(x) has a local maximum value at x c, can anything be said about h at the value x = - c? Give reasons for your answer.
2) Suppose that g" is continuous on [a, b] and that g has three zeros in the interval. Show that g" has at least one zero in (a, b). Generalize your result.
3) Explain why the following statements are true or false:
a) If fis continuous on [2, 5] and differentiable on (2, 5), and f(2)
o, then there is a number c between 2 and 5 where f '(c)
o and f5)
o.
=
b) Iffis continuous on [2, 5] then there is an absolute maximum and an absolute minimum on [2, 5].
c) Iffis continuous on [2, 5] and differentiable on (2, 5), andf(2) = 6 and f(5) = 15, then there is a number c between 2 and 5 wheref '(c) = 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67342b98-e0ce-4ae8-aa29-a836333c63e3%2Fbb31f64d-5efc-41d0-bab9-6cbc445c3d7a%2F4fxl2b.png&w=3840&q=75)
Transcribed Image Text:1) If an odd function h(x) has a local maximum value at x c, can anything be said about h at the value x = - c? Give reasons for your answer.
2) Suppose that g" is continuous on [a, b] and that g has three zeros in the interval. Show that g" has at least one zero in (a, b). Generalize your result.
3) Explain why the following statements are true or false:
a) If fis continuous on [2, 5] and differentiable on (2, 5), and f(2)
o, then there is a number c between 2 and 5 where f '(c)
o and f5)
o.
=
b) Iffis continuous on [2, 5] then there is an absolute maximum and an absolute minimum on [2, 5].
c) Iffis continuous on [2, 5] and differentiable on (2, 5), andf(2) = 6 and f(5) = 15, then there is a number c between 2 and 5 wheref '(c) = 3.
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