1. Assume that f is continuous and differentiable on (-∞, ∞). consider the interval [a,b] where acb are real numbers. Determine whether the fo |lowing Statements are TRUE or FALSE and explain in 2-3 sentences a) There is a number c in Hhe interval [a,6] Such that f(c) is the absolute minimum of f on [a,b]. b) There is a number c in the interval (a,b) such that f'(c)= 0 c) If f(6)<7< f (a), then there exists a number c in the interval' (a,b) such that f(C) =7 d) If f(a) = 7 $ f(b) = 0, then there exists a number c in the interval (a,b) such that f'lc) = 아디 %3D
1. Assume that f is continuous and differentiable on (-∞, ∞). consider the interval [a,b] where acb are real numbers. Determine whether the fo |lowing Statements are TRUE or FALSE and explain in 2-3 sentences a) There is a number c in Hhe interval [a,6] Such that f(c) is the absolute minimum of f on [a,b]. b) There is a number c in the interval (a,b) such that f'(c)= 0 c) If f(6)<7< f (a), then there exists a number c in the interval' (a,b) such that f(C) =7 d) If f(a) = 7 $ f(b) = 0, then there exists a number c in the interval (a,b) such that f'lc) = 아디 %3D
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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![1. Assume that f is continuous and differentiable
on (-∞, ∞).consider the interval [a,b] where acb
are real numbers. Determine whether the fo |lowing
Statements are TRUE or FALSE and explain in 2-5
sentences
a) There is a number c in Hhe interval [a,6] Such
that f(c) is the absolute minimum of f on [a,b].
b) There is a number c in the interval (a,b) such that
f'(c) =0
c) If f(6)<7< f(a), then there exists a number
c in the interval' (a,b) such that f(C)=7
d) If f(a) = 7 $ f(b) = 0, then there exists a
number c in the interval (a,b) such that
f'(c) = 아디
%3D
그](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fbff82e-583d-4003-b329-07736a7bbd92%2F434f6ad9-37ff-4d12-b137-39a6ba8ca762%2Fx5osmus_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Assume that f is continuous and differentiable
on (-∞, ∞).consider the interval [a,b] where acb
are real numbers. Determine whether the fo |lowing
Statements are TRUE or FALSE and explain in 2-5
sentences
a) There is a number c in Hhe interval [a,6] Such
that f(c) is the absolute minimum of f on [a,b].
b) There is a number c in the interval (a,b) such that
f'(c) =0
c) If f(6)<7< f(a), then there exists a number
c in the interval' (a,b) such that f(C)=7
d) If f(a) = 7 $ f(b) = 0, then there exists a
number c in the interval (a,b) such that
f'(c) = 아디
%3D
그
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