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. Suppose p is in the domain of f: • f has a local minimum at x = p if ƒ(p) is less than or equal to the values of f for points near P. • f has a local maximum at x = p if f(p) is greater than or equal to the values of f for points near p. Come up with an example of a function f and a value for p so that f has both a local minimum and a local maximum when x = p. Then explain in sentences how your example satisfies both definitions above. (Hint: Notice the word equal in the definitions above.)

. Suppose p is in the domain of f: • f has a local minimum at x = p if ƒ(p) is less than or equal to the values of f for points near P. • f has a local maximum at x = p if f(p) is greater than or equal to the values of f for points near p. Come up with an example of a function f and a value for p so that f has both a local minimum and a local maximum when x = p. Then explain in sentences how your example satisfies both definitions above. (Hint: Notice the word equal in the definitions above.)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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1. Suppose p is in the domain of f: f has a local minimum at x = p if f(p) is less than or equal to the values of f for points near P. f has a local maximum at x = p if f(p) is greater than or equal to the values of f for points near p. Come up with an example of a function f and a value for p so that f has both a local minimum and a local maximum when x = p. Then explain in sentences how your example satisfies both definitions above. (Hint: Notice the word equal in the definitions above.)
Transcribed Image Text:1. Suppose p is in the domain of f: f has a local minimum at x = p if f(p) is less than or equal to the values of f for points near P. f has a local maximum at x = p if f(p) is greater than or equal to the values of f for points near p. Come up with an example of a function f and a value for p so that f has both a local minimum and a local maximum when x = p. Then explain in sentences how your example satisfies both definitions above. (Hint: Notice the word equal in the definitions above.)
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