Let f be a continuous function defined on the closed interval [a,b] and differentiable on the open interval (a,b). Which of the following statements is true? a) If f(c)is the absolute minimum of fon [a,b],for c (a,b), then it is a relative minimum. b) If f has no relative extrema on (a,b), then it has no absolute extrema on [a,b]. c) If f(c) is a relative maximum, for c= (a,b),then f(c)is the absolute maximum of fon [a,b]. d) If f(a)=f(b) then the absolute maximum of f on [a,b] is the same as the absolute minimum of f on [a,b].
Let f be a continuous function defined on the closed interval [a,b] and differentiable on the open interval (a,b). Which of the following statements is true? a) If f(c)is the absolute minimum of fon [a,b],for c (a,b), then it is a relative minimum. b) If f has no relative extrema on (a,b), then it has no absolute extrema on [a,b]. c) If f(c) is a relative maximum, for c= (a,b),then f(c)is the absolute maximum of fon [a,b]. d) If f(a)=f(b) then the absolute maximum of f on [a,b] is the same as the absolute minimum of f on [a,b].
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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![Let f be a continuous function defined on the closed interval [a,b] and differentiable
on the open interval (a,b). Which of the following statements is true?
a) If f(c)is the absolute minimum of fon [a,b],for c (a,b), then it is a relative minimum.
b) If f has no relative extrema on (a,b), then it has no absolute extrema on [a,b].
c) If f(c) is a relative maximum, for c= (a,b),then f(c)is the absolute maximum of
fon [a,b].
d) If f(a)=f(b) then the absolute maximum of f on [a,b] is the same as the
absolute minimum of f on [a,b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F108f8a6c-2955-46fa-b885-667817ffe50f%2F277a1fbd-8cff-458e-ba63-24b157ae220c%2Fkwj92kd_processed.png&w=3840&q=75)
Transcribed Image Text:Let f be a continuous function defined on the closed interval [a,b] and differentiable
on the open interval (a,b). Which of the following statements is true?
a) If f(c)is the absolute minimum of fon [a,b],for c (a,b), then it is a relative minimum.
b) If f has no relative extrema on (a,b), then it has no absolute extrema on [a,b].
c) If f(c) is a relative maximum, for c= (a,b),then f(c)is the absolute maximum of
fon [a,b].
d) If f(a)=f(b) then the absolute maximum of f on [a,b] is the same as the
absolute minimum of f on [a,b].
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