Assume fis differentiable and has just one critical point, at x = 3. In parts (a)- (d), you are given additional conditions. In each case decide whether x = 3 is a local maximum, a local minimum, or neither. You should be able to sketch possible graphs for all four cases. (a) f(1) 3 and f(5)= -3 Ox-3 is a local maximum. Ox= 3 is a local minimum Ox-3 is neither a local maximum nor a local minimum. lim fx) and lim f(x)= Ox-3 is a local maximum. Ox= 3 is a local minimum Ox= 3 is neither a local maximum nor a local minimum. (b) lim (c) f(1) = 2, f(2)= 3, f(4) = 4, and (5) = 5 Ox= 3 is a local maximum. Ox-3 is a local minimum Ox-3 is neither a local maximum nor a local minimum.
Assume fis differentiable and has just one critical point, at x = 3. In parts (a)- (d), you are given additional conditions. In each case decide whether x = 3 is a local maximum, a local minimum, or neither. You should be able to sketch possible graphs for all four cases. (a) f(1) 3 and f(5)= -3 Ox-3 is a local maximum. Ox= 3 is a local minimum Ox-3 is neither a local maximum nor a local minimum. lim fx) and lim f(x)= Ox-3 is a local maximum. Ox= 3 is a local minimum Ox= 3 is neither a local maximum nor a local minimum. (b) lim (c) f(1) = 2, f(2)= 3, f(4) = 4, and (5) = 5 Ox= 3 is a local maximum. Ox-3 is a local minimum Ox-3 is neither a local maximum nor a local 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:Assume f is
differentiable and has just one critical point, at x = 3. In parts (a) - (d), you are given additional conditions. In each case decide whether x = 3 is a local maximum, a local minimum, or neither. You should be able to sketch possible graphs for all four cases.
(a) f(1) = 3 and f'(5) = -3
O x = 3 is a local maximum.
O x = 3 is a local minimum
O x = 3 is neither a local maximum nor a local minimum.
(b) lim f(x) = ∞ and lim f(x) = 00
X→∞0
X-8
O x = 3 is a local maximum.
O x = 3 is a local minimum
O x = 3 is neither a local maximum nor a local minimum.
(c) f(1) = 2, f(2)= 3, f(4) = 4, and f(5) = 5
O x = 3 is a local maximum.
O x = 3 is a local minimum
O x = 3 is neither a local maximum nor a local minimum.
(d) f'(2) = -1, f(3) = 1, and lim f(x) = 3
x → ∞
O x = 3 is a local maximum.
O x = 3 is a local minimum
O x = 3 is neither a local maximum nor a local minimum.
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