kindly do it fast Let F(x) = (f(x))²+ (f'(x))², F(0) = 6, where f(x) is a thrice differentiable functionsuch that |f(x)| < Vx E [-1, 1], then choose the correct statement(s)(A) there is atleast one point in each of the intervals (-1,0) and (0,1) where [f'(x)|<2(B) there is atleast one point in each of the intervals (-1,0) and (0,1) where F(x)< 5(C) there is no point of local maxima of F(x) in (-1, 1)(D) for some c E (-1, 1), F(c) > 6, F'(c) = 0 and F"(c) < 0

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Answered: Let F(x) = (f(x))² + (f'(x))², F(0) =…

Let F(x) = (f(x))² + (f'(x))², F(0) = 6, where f(x) is a thrice differentiable function such that |f(x)| 6, F'(c) = 0 and F"(c) <0

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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Question

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kindly do it fast

Let F(x) = (f(x))²+ (f'(x))², F(0) = 6, where f(x) is a thrice differentiable function
such that |f(x)| < Vx E [-1, 1], then choose the correct statement(s)
(A) there is atleast one point in each of the intervals (-1,0) and (0,1) where [f'(x)|<2
(B) there is atleast one point in each of the intervals (-1,0) and (0,1) where F(x)< 5
(C) there is no point of local maxima of F(x) in (-1, 1)
(D) for some c E (-1, 1), F(c) > 6, F'(c) = 0 and F"(c) < 0

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