FDT. Given a function f(x) defined in a neighborhood of a critical point x = c, the first derivative test states O if f'(x) < 0 for x 0 for x > C, then x = c is a relative minimum O if f'(x) > 0 for x < c and f'(x) > 0 for x > C, then x = c is a relative maximum O none of the other answers O if f'(x) < 0 for x C, and f'(c) = 0, then x = c is a relative maximum O if f'(x) < 0 for x 0 for x > C, then x = c is a relative maximum O if f'(x) > 0 for x C, then x = c is a relative minimum O if f'(x) > 0 for x 0 for x> C, and f'(c) = 0, then x = c is a relative minimum O if f'(x) > 0 for x < c and f'(x) > 0 for x > C, and f'(c) = 0, then x = c is a relative maximum O if f'(r) r 0 for x C, and f'(c) = 0, then x= cis a relative minimum
FDT. Given a function f(x) defined in a neighborhood of a critical point x = c, the first derivative test states O if f'(x) < 0 for x 0 for x > C, then x = c is a relative minimum O if f'(x) > 0 for x < c and f'(x) > 0 for x > C, then x = c is a relative maximum O none of the other answers O if f'(x) < 0 for x C, and f'(c) = 0, then x = c is a relative maximum O if f'(x) < 0 for x 0 for x > C, then x = c is a relative maximum O if f'(x) > 0 for x C, then x = c is a relative minimum O if f'(x) > 0 for x 0 for x> C, and f'(c) = 0, then x = c is a relative minimum O if f'(x) > 0 for x < c and f'(x) > 0 for x > C, and f'(c) = 0, then x = c is a relative maximum O if f'(r) r 0 for x C, and f'(c) = 0, then x= cis a relative minimum
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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Transcribed Image Text:FDT. Given a function f(x) defined in a nelghborhood of a critical point x= c, the first derivative test states that:
O if f (x) < 0 for x <c and f'(x) > 0 for x > c, then x c is a relative minimum
O if f'(x) > 0 for x < c and f'(x) > 0 for x > C, then x = c is a relative maximum
O none of the other answers
O if f'(x) < 0 for x < c and f (x) < 0 for x > c, and f'(c) = 0, then x = c is a relative maximum
%3D
O if f'(x) < 0 for x < c and f'(x) > 0 for x > c, then x = c is a relative maximum
O if f(x) > 0 for x <c and f'(x) < 0 for x > C, then x = c is a relative minimum
%3D
O if f'(x) > 0 for x <c and f (x) > 0 for x > C, and f'(c) = 0, then x = cis a relative minimum,
O if f'(x) > 0 for x < c and f'(x) > 0 for x > c, and f'(c) = 0, then x = c is a relative maximum
O if f'(x) < 0 for x <c and f (x) < 0 for x C, and f'(c) = 0, then x = cis a relative minimum
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