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Get Full Access to College Algebra - 9 Edition - Chapter 9.3 - Problem 29
Get Full Access to College Algebra - 9 Edition - Chapter 9.3 - Problem 29

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9th term of 1, -1, 1

ISBN: 9780321716811 485

Solution for problem 29 Chapter 9.3

College Algebra | 9th Edition

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College Algebra | 9th Edition

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Problem 29

9th term of 1, -1, 1,

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Step 1 of 3

Minimum and maximum values Let c be a number in the domain of f. f(c) is a local max if f(c) ≥ f(x) when x is near c. f(c) is a local min if f(c) ≤ f(x) when x is near c Fermat’s Theorem: ​If f has a local max or min at c, and if f’(c) exists, then f’(c)’=0 Be careful: The converse of this theorem is not always true. Consider f(x) = x^3 f’(x) = 3x^2 f’(0) = 3*0^2 =0 However there is no min/ max at x=0 the tangent line is horizontal there. Consider f(x) = [x] F has a minimum at x = 0; however f’(0) does not exist. Consider f(x) = √x f has a minimum at x = 0 f’(x) = 1/√x f’(0) = 1/2 0 d oes not exist The tangent line is vertical there Def. a critical number of a function f is a number c in the domain of f such that either f’(c) = 0 or f

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9th term of 1, -1, 1