Suppose f(x) = g(x)/3 where g is twice differentiable on (1, o) and g(x) > 0, g' (x) > 0, g" (x) < 0 for all x>1. Which of the following statements must be true? HINT: Can you think of such a function? f has at least one point of inflection. f has at least one critical point. fis concave un on (1 om)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Suppose f(x) = g(x)/3 where g is twice differentiable on (1, o) and
g(x) > 0, g' (x) > 0, g" (x) < 0 for all x>1. Which of the following statements must
be true?
HINT: Can you think of such a function?
f has at least one point of inflection.
Of has at least one critical point.
Of is concave up on (1, co).
Of is decreasing on (1, a) for some constant a>1.
Of is discontinuous.
Of is concave down on(1, o).
Transcribed Image Text:Suppose f(x) = g(x)/3 where g is twice differentiable on (1, o) and g(x) > 0, g' (x) > 0, g" (x) < 0 for all x>1. Which of the following statements must be true? HINT: Can you think of such a function? f has at least one point of inflection. Of has at least one critical point. Of is concave up on (1, co). Of is decreasing on (1, a) for some constant a>1. Of is discontinuous. Of is concave down on(1, o).
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