The set of rational numbers is the set of numbers of the form p q , where p and q are and q 0.
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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
Textbook: A Survey of Mathematics with Applications
Author: Allen R. Angel, Christine D. Abbott, Dennis C. Runde
Since the solution to 5.1.178 from 5.3 chapter was answered, more than 277 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9. This full solution covers the following key subjects: . This expansive textbook survival guide covers 105 chapters, and 6968 solutions. The full step-by-step solution to problem: 5.1.178 from chapter: 5.3 was answered by , our top Math solution expert on 12/28/17, 08:33PM. The answer to “The set of rational numbers is the set of numbers of the form p q , where p and q are and q 0.” is broken down into a number of easy to follow steps, and 24 words. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665.