Minimum Definition and 1000 Threads

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. G

    Quantum Dr Susskind: Theoretical Minimum Quantum Field Theory?

    Does anyone know if or when Dr Susskind is coming out with a “ Theoretical Minimum Quantum Field Theory “ ?
  2. M

    Shoot a basketball with a minimum speed at some angle

    Homework Statement You should shoot a basketball at the angle ##\theta## requiring minimum speed. Avoid line drives and rainbows. Shooting from (0, 0) with the basket at (a, b), minimize ##f(\theta)= 1/(a \sin (\theta) \cos (\theta) -b \cos^2 (\theta))##. (a) If b =0 you are level with the...
  3. R

    When is the minimum polynomial of a scalar matrix kI equal to t-k?

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  4. synMehdi

    A Pontryagin minimum principle with control constraints

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  5. Physics345

    Minimum cost of an area of fencing using derivatives

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  6. C

    Proving Snell's law using Euler-Lagrange equations

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  7. S

    Minimum force to separate two oppositely-charged ions

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  8. T

    Finding minimum and maximum intensity of waves

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  9. bbbl67

    I What is theoretical minimum mass of neutronium?

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  10. Alexanddros81

    Calculate the maximum and minimum distances between the Earth and the Moon

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  11. Sheldon11

    B Why do we have minimum deviation of a prism?

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  12. V

    Minimum and maximum resultant of three vectors.

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  13. K

    Calculate the minimum uncertainty

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  14. Peter Alexander

    How to determine minimum amount of AND and OR gates in PLA?

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  15. G

    DNA testing, what kind of sample is the minimum?

    Is it possible to do DNA test from fallen hair, or skin cells? Or no, since the cells die and lose their core before they fall from the body? Do dead cells still have somekind of unique "fingerprint"?
  16. J

    DC Distribution System -- Minimum Voltage across the line

    Homework Statement Homework Equations V = IR And R becomes 2(r of one conductor) because of return path. The Attempt at a Solution V minimum is at third junction. At VD Using KVL we get: [/B] Drop at AB = (10 + 20 + 50) * 2 * 0.1 = 16 V Drop at BC = (20 + 50) * 2 * 0.08 = 11.2 Drop at CD =...
  17. V

    Minimum friction to roll an imperfect sphere on an incline

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  18. bbbl67

    I What is the minimum mass of a neutron star?

    We just discovered the maximum mass of a neutron star, discovered after the recent neutron star merger event back in Aug. They say that the maximum mass of a neutron star is approximately 2.16 solar masses. So I always assumed that the lowest mass for one is 1.4 solar masses, the Chandresekhar...
  19. Roger Dodger

    B Least / Smallest / Minimum Detectable Difference

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  20. M

    MHB How Can We Find the Minimum 2-Norm of Ax-y Using an Orthogonal Matrix?

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  21. Richie Smash

    Inequality to represent minimum monthly income.

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  22. BiGyElLoWhAt

    I Minimum number of moves from a to b

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  23. X

    Maximum and minimum tensile/compressive strain in beam

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  24. Abhimessi10

    Finding the minimum time for crossing a river

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  25. Pushoam

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  26. kandelabr

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  27. EastWindBreaks

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  28. T

    Shear force for minimum links is greater than the maximum sh

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  29. T

    Calculate minimum work input of refrigeration cycle

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  30. Y

    What Is the Minimum Stopping Distance to Prevent Crate Sliding?

    Homework Statement A crate is being transported on a flatbed truck. The coefficient of static friction between the crate and the bed is 0.470. What is the minimum stopping distance if the truck, traveling at 70 km/h, is to decelerate uniformly and the crate is not to slide forward on the bed...
  31. K

    What is the Proof for Local Minimum and Maximum at First Derivative Equals Zero?

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  32. A

    Minimum spring force required to keep a car level

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  33. Oannes

    Finding Minimum Force Needed to Hold Object In Place

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  34. Muthumanimaran

    Minimum work needed to compensate for a heat leak

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  35. Noisy Rhysling

    Minimum population needed to keep an anthropoid creature....

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  36. T

    Maximum entropy principle from minimum energy principle

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  37. M

    MHB Negative minimum of the average variable cost function

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  38. M

    What is the minimum speed required for Spiderman to catch a falling baby?

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  39. Pushoam

    Minimum acceleration of a car at which front wheels leave the ground

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  40. B

    What is the minimum number of H+ ions required during ATP production?

    how many minimum number of H+ ions are required during ATP production in citric acid cycle (CAC)?
  41. lfdahl

    MHB Find the minimum a^4+b^4+c^4−3abc

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  42. I

    Minimum Mass required to lift up an object from a spring

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  43. A

    Minimum h for Car to Remain on Track Around Loop

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  44. A

    I Max and min values -- Finding them in a data set

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  45. J

    Minimum value of coefficient of friction

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  46. Const@ntine

    Wave Interference: Minimum Intensity/Hyperbolic

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  47. |Glitch|

    B What is the relationship between brown dwarfs and giant gas planets?

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  48. K

    B Calculus of variation. Minimum surface

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  49. E

    How Do You Calculate the Force Needed to Prevent a Block from Sliding on a Wall?

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  50. T

    Arranging resistors to have a minimum equivalent

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