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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

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
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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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
Transcribed Image Text: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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