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Select the true statements regarding a graph of f and its derivatives. □ If f'(c) · ƒ" (c) = 0, then (c, f(c)) is a local extreme value. If f' and f" have signs that change from +- to -- at x = c, then ƒ has a local maximum at c. □ If ƒ' > 0 and ƒ" < 0 on the interval I, then the graph of the function is increasing and concave up on I. □ If ƒ"(c) = 0, then (c, f(c)) is a point of inflection. □ If ƒ' · ƒ" > 0, then ƒ is increasing at an increasing rate, or f is decreasing at a decreasing rate.

Select the true statements regarding a graph of f and its derivatives. □ If f'(c) · ƒ" (c) = 0, then (c, f(c)) is a local extreme value. If f' and f" have signs that change from +- to -- at x = c, then ƒ has a local maximum at c. □ If ƒ' > 0 and ƒ" < 0 on the interval I, then the graph of the function is increasing and concave up on I. □ If ƒ"(c) = 0, then (c, f(c)) is a point of inflection. □ If ƒ' · ƒ" > 0, then ƒ is increasing at an increasing rate, or f is decreasing at a decreasing rate.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Select the true statements regarding a graph of f and its derivatives. If f'(c) f"(c) = 0, then (c, f(c)) is a local extreme value. If f' and f" have signs that change from +- to -- at x = c, then f has a local maximum at c. If f'> 0 and f" <0 on the interval I, then the graph of the function is increasing and concave up on I. If f" (c) = 0, then (c, f(c)) is a point of inflection. □ If ƒ' · ƒ" > 0, then ƒ is increasing at an increasing rate, or f is decreasing at a decreasing rate.
Transcribed Image Text:Select the true statements regarding a graph of f and its derivatives. If f'(c) f"(c) = 0, then (c, f(c)) is a local extreme value. If f' and f" have signs that change from +- to -- at x = c, then f has a local maximum at c. If f'> 0 and f" <0 on the interval I, then the graph of the function is increasing and concave up on I. If f" (c) = 0, then (c, f(c)) is a point of inflection. □ If ƒ' · ƒ" > 0, then ƒ is increasing at an increasing rate, or f is decreasing at a decreasing rate.
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