Suppose f'(x) is continuous over an interval a < x < b, and a < c

For f'(c) = -9f(c) = -9 (not sure, not necessary)f does not have minima at c, this is applicable,As…

Answered: Suppose f'(x) is continuous over an…

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Calculus

Suppose f'(x) is continuous over an interval a

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.2: Polynomial Functions

Problem 96E: What is the purpose of the Intermediate Value Theorem?

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

100%

Suppose f'(x) is continuous over an interval a < x < b, and a < c <d < b.
If f'(c)
O f(c) = - 9
- 9, then (check all that apply)
%3D
Of does not have a minimum at æ = c
O f(c) exists
Of does not have a maximum at x = c
O f(x) is decreasing through x = c
O f(x) is increasing through a = c
Hint: Be sure to check ALL that apply
If f'(d) = 6, then (check all that apply)
O f(x) is decreasing through z =
O f(x) is increasing through a =
d
If does not have a minimum at a =
d
O f(d) exists
O f(d) = 6
Of does not have a maximum at = d
Hint: Be sure to check ALL that apply
Based on this, we know that for some x between I = c and x = d:
O f'(x) = 0
Of has a maximum
Of does not exist
Vf has a minimum

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