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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.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?
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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.
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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