Let f be a function defined and continuous on the closed interval [a, b]. If ƒ has a relative maximum at c and a < c < b, which of the following statements must be true? l. fi (c) exists II. If f (c) exists, then f (c) = 0 III. If fil (c) exists, then fll (c) ≤ 0. III only O I and II only II and III only Il only

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Let f be a function defined and continuous on the closed interval [a, b]. If ƒ has a
relative maximum at c and a < c < b, which of the following statements must be
true?
1. fl (c) exists
II. If fl (c) exists, then fꞌ (c) = 0
III. If fll (c) exists, then fll (c) ≤ 0.
III only
I and II only
O II and III only
O II only
Transcribed Image Text:Let f be a function defined and continuous on the closed interval [a, b]. If ƒ has a relative maximum at c and a < c < b, which of the following statements must be true? 1. fl (c) exists II. If fl (c) exists, then fꞌ (c) = 0 III. If fll (c) exists, then fll (c) ≤ 0. III only I and II only O II and III only O II only
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