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. Saracen Rue

    I How to find the maximum arc length of this equation?

    After seeing a discussion about graphs of the relationship ##x^x + y^y = r^r##, it got me interested in attempting to see what the graphical appearance of ##{^{\infty}x}+{^{\infty}y}={^{\infty}r}## would look like. The first step I did was use the relationship of...
  2. I

    What is the maximum charge in Coulombs can be obtained in ionistor?

    What is the maximum charge in coulombs can be obtained on the plates of ionistors like these: https://en.wikipedia.org/wiki/Supercapacitor ?
  3. M

    MHB How Can Carl Use Maximum a Posteriori to Estimate His Book Preferences?

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  4. L

    Need a Hand Calculating the Maximum Load on a Structure

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  5. F

    How Does Eddington Luminosity Limit Black Hole Mass Accretion Rates?

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  6. jisbon

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  7. Stephen Miller

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  8. A

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  9. Fran

    Calculate the maximum force on a wheel passing over an obstacle?

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  10. M

    Engineering Homework: Rx=? to get maximum power transfer at point M

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  11. S

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  12. Addez123

    Find Wavelength of Light Wave for Optimal Constructive Interference

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  13. A

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  14. M

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  15. Arman777

    I Maximum ##d_p(t_e)## value and its meaning

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  16. Adrian Tudini

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  17. Physics lover

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  18. F

    What is the maximum current in a superconductor loop?

    If we put an emf equal constant onto a superconductor loop(we consider the resister of emf equal zero), then what is the maximum of current in the loop?
  19. Cerenkov

    B What are the maximum masses of White Dwarves and of Neutron stars?

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  20. Prialen

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  21. H

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  22. E

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  23. Q

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  24. S

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  25. V

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  26. S

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  27. L

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  28. WMDhamnekar

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  30. A

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  31. T

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  32. R

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  33. M

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  34. H

    I How do you exactly calculate the theoretical maximum efficiency of an LED?

    Hi! I found interesting post here: https://electronics.stackexchange.com/questions/325762/how-efficient-are-leds However, it only gives the final results and not the steps he made. I tried to learn the formulas on wikipedia on my own but I couldn't figure out what variables need to have what...
  35. paulmdrdo

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    I was able to find the maximum value for this function by differentiating and equating it to zero and find the time t and substitute it back to the original expression to get the max amplitude. tm = -0.001012 s v(tm) = 56.6 Another method that was presented in my book was can you explain how...
  36. M

    Engineering Induction Motor's Speed at Maximum Torque

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  37. Astrogirl101

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  38. M

    How can I find the width of the central diffraction maximum.

    If I am given the width of the slit (b), wavelength of the light (λ), and the distance of the slit from the screen (D), how can I find the width of the central maximum (d)? My book says d/2=Dλ/b, but with no explanation and I don't understand why. Where does this formula come from? Thank you...
  39. melel

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  40. Rituraj131

    Maximum Capillary Rise: Dynamic Treatment of Liquid in Motion?

    I know that the height in general is goven by 2σcos(θ)/(ρgr). So the maximum height can be 2σ/(ρgr) with cos(θ)=1. But the answer given is c.
  41. T

    Slab resting on two supports: Maximum weight added without tipping?

    Hi, My attempted solution is in the image: I choose the edge on the left side, but the solution should be similar on both sides (just substitute C for A). (I missed to multiply by "g" in F_2.) Is this the correct way of thinking? I'm not sure about the distance "D".
  42. C

    Automotive Front Wheel Drive or Rear Wheel Drive has higher maximum slip ratio?

    The graph is relationship between longitudinal force and slip ratio under the conditions of 0 longitudinal acceleration and flat road(0 angle of inclination). Which line represent FWD or RWD? Does FWD or RWD have higher maximum slip ratio?
  43. T

    Maximum height for water from a fire hose

    Homework Statement Fire hose has diameter of 4.0 cm and flow rate of 10 L/s. There is pressure of 2.2 bar inside the hose. How high the water can go at best? Water density is 1.00E3 kg/m^3 and air pressure outside the hose is 1.0 bar. Homework Equations Flow rate $$ Q = Av $$ Newtons...
  44. F

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  45. F

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    Homework Statement A block is suspended by an ideal spring of the force constant K. If the block is pulled down by applying a constant force F and if maximum displacement of the block from its initial position of rest is X then, find the value of X. Homework Equations mg + F = XK + K(mg/K)...
  46. X

    Calculate the maximum voltage that can be applied

    Homework Statement A detector of radiation called a Geiger-Muller counter consists of a closed, hollow, conducting cylinder with a fine wire along its axis. Suppose that the internal diameter of the cylinder is 3.00 cm and that the wire along the axis has a diameter of 0.2 mm. If the dielectric...
  47. Yasin

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  48. R

    Projectile motion -- Maximum range it can travel inside a 2m tunnel

    Homework Statement A particle is projected inside a tunnel which is 2 m high and must not hit the side or ceiling of the tunnel. If the initial speed is U show that the maximum range of the particle inside the tunnel You may assume that the maximum range is attained when the projectile just...
  49. S

    Why is there no maximum temperature?

    Given that absolute zero is the lowest temperature possible, were all particles have zero vibration. And given that the speed of light is the highest speed any object, particle, sub atomic or not can travel. Using 2 of the most fundamental laws of physics thermodynamics and general relativity...
  50. Q

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