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A differentiable function g(x) has only one local maxima at x = 1. It is also known that g" (1) < 0. Which of the following statements must be TRUE? • Statement A: g'(1) = 0 Statement B: g(x) > 0 on (-∞, 1) and g'(x) <0 on (1,∞) Select one alternative: OB only None Both A and B O A only

A differentiable function g(x) has only one local maxima at x = 1. It is also known that g" (1) < 0. Which of the following statements must be TRUE? • Statement A: g'(1) = 0 Statement B: g(x) > 0 on (-∞, 1) and g'(x) <0 on (1,∞) Select one alternative: OB only None Both A and B O A only

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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A differentiable function g(x) has only one local maxima at x = 1. It is also known that g" (1) < 0. Which of the following statements must be TRUE? • Statement A: g'(1) = 0 ● Statement B: g'(x) > 0 on (-∞,1) and g'(x) <0 on (1,∞) Select one alternative: O B only O None O Both A and B O A only
Transcribed Image Text:A differentiable function g(x) has only one local maxima at x = 1. It is also known that g" (1) < 0. Which of the following statements must be TRUE? • Statement A: g'(1) = 0 ● Statement B: g'(x) > 0 on (-∞,1) and g'(x) <0 on (1,∞) Select one alternative: O B only O None O Both A and B O A only
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