What Are the Max and Min Values of the Function f(x) = 1/3X^3 - 1/2^2 - 6x + 4?

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Discussion Overview

The discussion revolves around the function f(x) = 1/3X^3 - 1/2^2 - 6x + 4, specifically addressing the concepts of maximum and minimum values, including local and global extrema.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant suggests that the maximum value is positive infinity and the minimum value is negative infinity.
  • Another participant counters that if considering local optima, it is more accurate to state that there is no global maximum or minimum rather than asserting they exist at infinity.
  • A third participant reiterates that the function is "unbounded" and has no global maximum or minimum.

Areas of Agreement / Disagreement

Participants express differing views on how to characterize the maximum and minimum values of the function, indicating a lack of consensus on the terminology and implications of infinity in this context.

Contextual Notes

There is ambiguity regarding the definitions of local versus global extrema and the implications of the function being unbounded.

physicszman
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consider function f(x) = 1/3X^3 - 1/2^2 - 6x + 4

maximum is positive infinity and minimum is negative infiniti correct?

Thank you!
 
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Not if you are looking for local optima. It might be better to say there is no global maximum or minimum, than it is at infinity, to avoid unnecessary use of infinity.
 
Originally posted by physicszman
consider function f(x) = 1/3X^3 - 1/2^2 - 6x + 4

maximum is positive infinity and minimum is negative infiniti correct?

Thank you!

I wouldn't put it that way. I would say that the function is "unbounded" and has no global maximum or minimum.
 
thanks for the help!
 

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