- #1
phymatter
- 131
- 0
what is the reason that the minima and maxima of ( ex2 -1 )1/2 and ( ex2 -1 ) are the same ??
Why Do (ex2-1)1/2 and (ex2-1) Have the Same Minima/Maxima?
- Context: Graduate
- Thread starter phymatter
- Start date
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Discussion Overview
The discussion centers on the relationship between the minima and maxima of the functions \( (ex^2 - 1)^{1/2} \) and \( (ex^2 - 1) \). Participants explore the underlying reasons for their equivalence in extrema, touching on concepts related to monotonic functions and their compositions.
Discussion Character
- Exploratory, Technical explanation, Conceptual clarification
Main Points Raised
- One participant questions the reason why the minima and maxima of \( (ex^2 - 1)^{1/2} \) and \( (ex^2 - 1) \) are the same.
- Another participant asks for methods to find the maxima and minima of a function, indicating a potential interest in calculus techniques.
- A different participant suggests that if \( g \) is a monotone increasing function, then the maxima and minima of \( g(f(x)) \) and \( f(x) \) will be the same, implying a theoretical framework for understanding the relationship between the two functions.
- This same participant reiterates the previous point, emphasizing the need for a proof of the claim regarding monotonic functions.
Areas of Agreement / Disagreement
Participants do not reach a consensus, and multiple viewpoints are presented regarding the relationship between the functions and the methods for finding extrema.
Contextual Notes
The discussion lacks detailed mathematical proofs or specific examples, and assumptions about the properties of the functions involved are not fully explored.
Who May Find This Useful
Individuals interested in calculus, function analysis, and the properties of monotonic functions may find this discussion relevant.
- #2
TylerH
- 729
- 0
How do you find the max and min of a function?
- #3
tiny-tim
Science Advisor
Homework Helper
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hi phymatter! 
this has nothing to do with calculus …
if g is a monotone increasing function, then the maxima and minima (and the local maxima and minima) of g(f(x)) and f(x) will be the same …
this has nothing to do with calculus …
if g is a monotone increasing function, then the maxima and minima (and the local maxima and minima) of g(f(x)) and f(x) will be the same …
now prove it! 
- #4
phymatter
- 131
- 0
tiny-tim said:hi phymatter!
this has nothing to do with calculus …
if g is a monotone increasing function, then the maxima and minima (and the local maxima and minima) of g(f(x)) and f(x) will be the same …
now prove it!
thanks tiny-tim! :)
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