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. R

    Determine maximum weight and angle for equilibrium

    Homework Statement The cords ABC and BD can each support a maximum load of 100 lb. Determine the weight of the crate, and the angle θ for equilibrium. Homework Equations ∑F= 0 ∑Fx=0 ΣFy=0 Setting derivative of an expression to zero To find critical point Second derivative test for determining...
  2. R

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  3. D

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  4. Nader AbdlGhani

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  5. C

    Where is the Local Maximum for y = (8/5)sin(t) + (4/5)cos(t) - (9/5)e^(-t/2)?

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  6. Dare Diamond

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  7. P

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  8. Keith

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  9. T

    Does a pump have a maximum flow rate for a given system?

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  10. V

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  12. L

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  13. ali nemati

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  14. O

    MHB Max A $\le$ Sup B: Is it True?

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  15. Luke Cohen

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  16. praveena

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  17. T

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  18. K

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  19. Julio1

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  20. E

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  21. Ketan Vadher

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  22. Tonia

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  23. S

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  24. AwesomeTrains

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  25. MidgetDwarf

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  26. C

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  27. Mayzu

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  28. freutel

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  29. P

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  30. C

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  31. T

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  32. Rafael de Gomes

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  33. M

    MHB Can the Maximum Principle be Used to Estimate Solutions of Elliptic Equations?

    Hey! :o Let $S=\{x \in \mathbb{R}^2 \mid |x| <1\}$. Using the maximum principle I have to show that the solution of the problem $$-\Delta u(x)=f(x), x \in S \\ u(x)=0, x \in \partial{S}$$ satisfies the estimation $$|u(x)| \leq \frac{1}{4}\max_{x \in \overline{S}} |f(x)|, x \in S$$ To use the...
  34. M

    MHB Maximum principle-Uniqueness of solution

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  35. M

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  36. S

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  37. L

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  38. S

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  39. S

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    What does it mean by maximum work of an isothermal, reversible expansion of a perfect gas from initial volume Vi to final volume Vf at temperature T? I understand that heat enters the system during this expansion to ensure that no internal energy is lost but it doesn't really help in anyway...
  40. Q

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  41. M

    MHB How Can Terrific Wears Inc. Maximize Revenue and Profit from Suit Sales?

    Terri c Wears Inc., a clothing rm determines that the demand for their suits is given by d = 2(175􀀀p), where d represents the demand and p represents the price of a suit. (Recall that Revenue=PriceDemand, Profi t=Revenue-Cost.) (1) Find the selling price for a suit that will generate maximum...
  42. J

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  43. S

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  44. S

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  45. M

    MHB Maximum Value of k in $(1+\frac{1}{a})(1+\frac{1}{b}) \ge k$ is 9

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  46. A

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  47. I

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  48. Satvik Pandey

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  49. C

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  50. J

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