Show that iff is differentiable on (a, b), and f'(c) > 0, where c E (a, b) and if f' is continuousat x = c, then there is an interval about c on which f is increasing 7. Show that if f is differentiable on (a, b), and f'(c) > 0, where ce (a, b) and if f' is continuousat x = c, then there is an interval about c on which f is increasing.

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Answered: 7. Show that if f is differentiable on…

7. Show that if f is differentiable on (a, b), and f'(c) > 0, where ce (a, b) and if f' is continuous at x = c, then there is an interval about c on which f is increasing.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Show that iff is differentiable on (a, b), and f'(c) > 0, where c E (a, b) and if f' is continuous
at x = c, then there is an interval about c on which f is increasing

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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