What is Maximum: Definition and 1000 Discussions

In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema), or on the entire domain (the global or absolute extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.
As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum.

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  1. AppleiPad556

    Maximum angle made by rotating hinge with energy and gravity

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  2. B

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  3. lonewolfx

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  4. L

    What is the maximum spring displacement?

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  5. Hamiltonian

    Find the maximum KE of a charged Disc

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  6. R

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  7. Moara

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  8. Grinkle

    B Maximum mass of a neutron star

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  9. duchuy

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  10. K

    I Theoretical maximum efficiency of a heat engine without Carnot

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  11. ORF

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  12. neilparker62

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  13. stephen8686

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  14. D

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  15. Sean Harold

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  16. D

    A Max Fidelity at $$F=|\langle\psi|\phi\rangle|^2$$

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  17. C

    Maximum safe mass of an asteroid in geostationary orbit

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  18. O

    I Maximum acceleration of an alpha particle?

    I would like to estimate the maximum acceleration (or deceleration) of an alpha particle that is backscattered by a heavy atom, like in Rutherford backscattering. I am interested in the order of magnitude, not in a precise value. I am assuming the collision is elastic. The kinetic energy of the...
  19. A

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  20. D

    I Maximum hole diameter to prevent water leakage

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  21. NSNS

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  22. L

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  23. Dario56

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  24. Mathman2013

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  25. H

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  26. Peter Jones

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  27. M

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  28. F

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  29. F

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  30. L

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  31. K

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  32. H

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  33. Strange07

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  34. brotherbobby

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  35. boysenbeary

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  36. M

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  37. A

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  38. J

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  39. C

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  40. J

    Help with best aerodynamic shape of undertray for maximum downforce?

    What is best theoretical shape of undertray for maximum downforce , maybe wing shape or venturi shape? classic "venturi shape" with diffuser "wing shape"
  41. J

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    First thank you for taking your time to take a look at this simple question. And sorry for the informal math language and equations, I hope you guys can understand it. So, depending on the case, I have 2 or 8 simple quadratic functions f(a), f(b), f(c),… f(z). Each a,b,c,…,z have a different...
  42. anemone

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    Find the maximum area of a pentagon $ABCDE$ inscribed in a unit circle such that the diagonal $AC$ is perpendicular to the diagonal $BD$.
  43. WMDhamnekar

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    Hi, Here is the question. Answer given is d. But i don't understand how is that computed? I am working on this question. Meanwhile any member knowing the correct answer may help me in finding out correct answer.
  44. A

    Maximum distance the airplane can cover

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  45. M

    MHB Orthonormal basis for the poynomials of degree maximum 2

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  46. S

    MHB Find Maximum of xyz: Real Solutions

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  47. S

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  48. C

    MHB Log likelihood and Maximum likelihood

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  49. L

    Maximum Induced Voltage of an AC Generator

    I would like to ask a question about the induced voltage of an AC generator. So, according to a graph I found on Google, the maximum induced voltage is reached when the loop is parallel to the loop. (The graph shown below.) Then I was wondering, what if the loop is initially (when it is at 0...
  50. cwill53

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