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Determine whether each statement is true or false, and explain why. The derivative in regions separated by critical numbers must alternate between positive and negative. A relative maximum is the greatest possible value of a function. A function has relative extrema at all critical numbers of the function. If a function is concave upward on an interval, it must be increasing on that interval. Acceleration is the instantaneous rate of change of velocity. If a function has an inflection point at x = c, then f"(c) = 0.

Determine whether each statement is true or false, and explain why. The derivative in regions separated by critical numbers must alternate between positive and negative. A relative maximum is the greatest possible value of a function. A function has relative extrema at all critical numbers of the function. If a function is concave upward on an interval, it must be increasing on that interval. Acceleration is the instantaneous rate of change of velocity. If a function has an inflection point at x = c, then f"(c) = 0.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 2E
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Determine whether each statement is true or false, and explain why. The derivative in regions separated by critical numbers must alternate between positive and negative. A relative maximum is the greatest possible value of a function. A function has relative extrema at all critical numbers of the function. If a function is concave upward on an interval, it must be increasing on that interval. Acceleration is the instantaneous rate of change of velocity. If a function has an inflection point at x = c, then f"(c) = 0.
Transcribed Image Text:Determine whether each statement is true or false, and explain why. The derivative in regions separated by critical numbers must alternate between positive and negative. A relative maximum is the greatest possible value of a function. A function has relative extrema at all critical numbers of the function. If a function is concave upward on an interval, it must be increasing on that interval. Acceleration is the instantaneous rate of change of velocity. If a function has an inflection point at x = c, then f"(c) = 0.
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