Suppose the derivative of the function y=f(x) is y'=(x-4)²(x-2). At what points, if any, does the graph of f have a local minimum, local maximum, or point of inflection? (Hint: Draw the sign pattern for y'.) At what points, if any, does the graph of f have a local minimum? OA. The graph has a local minimum at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. The graph has no local minimum. At what points, if any, does the graph of f have a local maximum? OA. The graph has a local maximum at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. The graph has no local maximum. At what points, if any, does the graph of f have a point of inflection? OA. The graph has a point of inflection at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. The graph has no point of inflection.
Suppose the derivative of the function y=f(x) is y'=(x-4)²(x-2). At what points, if any, does the graph of f have a local minimum, local maximum, or point of inflection? (Hint: Draw the sign pattern for y'.) At what points, if any, does the graph of f have a local minimum? OA. The graph has a local minimum at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. The graph has no local minimum. At what points, if any, does the graph of f have a local maximum? OA. The graph has a local maximum at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. The graph has no local maximum. At what points, if any, does the graph of f have a point of inflection? OA. The graph has a point of inflection at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. The graph has no point of inflection.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...
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Transcribed Image Text:Suppose the derivative of the function y = f(x) is y' = (x − 4)²(x - 2). At what points, if any, does the graph of f have a local minimum, local maximum, or point of inflection? (Hint: Draw the sign pattern for y'.)
At what points, if any, does the graph of f have a local minimum?
OA. The graph has a local minimum at x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
O B. The graph has no local minimum.
At what points, if any, does the graph of f have a local maximum?
OA. The graph has a local maximum at x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. The graph has no local maximum.
At what points, if any, does the graph of f have a point of inflection?
OA. The graph has a point of inflection at x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. The graph has no point of inflection.
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