1. (Applies to Standards T1 and T2) 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 %3D near p. • f has a local maximum at r = p if f(p) is greather 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 whenr= p. Then explain in sentences how your example satisfies both definitions above. ATTRIBUTES OF EDITION 2. (Applies to Standards T3 and D2) Generate a counterexample to show that the statement below is falsc. Explain why your example is a counter example to the statement. (Hint: make sure your answer demonstrates your competence with both standards T3 and D2.) If an object has a negative acceleration, then its velocity must also be negative.

1. (Applies to Standards T1 and T2) 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 %3D near p. • f has a local maximum at r = p if f(p) is greather 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 whenr= p. Then explain in sentences how your example satisfies both definitions above. ATTRIBUTES OF EDITION 2. (Applies to Standards T3 and D2) Generate a counterexample to show that the statement below is falsc. Explain why your example is a counter example to the statement. (Hint: make sure your answer demonstrates your competence with both standards T3 and D2.) If an object has a negative acceleration, then its velocity must also be negative.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

life
1. (Applies to Standards T1 and T2)
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 r = p if f(p) is greather 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 whenr = p. Then explain in sentences how your example satisfies both
definitions above.
TU
ATTRIBUTES OF LIN
EDITION
2. (Applies to Standards T3 and D2)
Generate a countercxample to show that the statement below is falsc. Explain why your cxample is
a counter example to the statement. (Hint: make sure your answer demonstrates your competence
with both standards T3 and D2.)
If an object has a negative acceleration, then its velocity must also be negative.

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