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Assume the function f is differentiable everywhere and has just one critical point, at x = 3. In each situation, determine if there is a local maximum, local minimum, or neither. Justify each with a sketch or words. f’(1) = 3 and f’(5) = -1 f’(2) = -1, f (3) = -1, and lim x→∞ f(x) = 3 f(3) = 1 and f ′(3) = −2

Assume the function f is differentiable everywhere and has just one critical point, at x = 3. In each situation, determine if there is a local maximum, local minimum, or neither. Justify each with a sketch or words. f’(1) = 3 and f’(5) = -1 f’(2) = -1, f (3) = -1, and lim x→∞ f(x) = 3 f(3) = 1 and f ′(3) = −2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Assume the function f is differentiable everywhere and has just one critical point, at x = 3. In each situation, determine if there is a local maximum, local minimum, or neither. Justify each with a sketch or words.

f’(1) = 3 and f’(5) = -1

f’(2) = -1, f (3) = -1, and lim x→∞ f(x) = 3

f(3) = 1 and f ′(3) = −2

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