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. F

    Maximum frequency, not bandwidth?

    Hey In many places on the Internet you can read how the Nyquist frequency must be at least as high as the signals bandwidth in order to properly reconstruct the signal. Isn't this a big misnomer, since it is not the bandwidth, but the highest frequency of the signal that determines the...
  2. G

    The maximum speed the truck can go without sliding

    Homework Statement A crate of eggs is located on the back of a truck. The truck rounds a circular bend in the road with radius of 35 meters. If the coefficient of static friction between the crate and the truck is 0.6, what is the maximum speed the truck can go without the crate...
  3. V

    Maximum tension between train cars, F=ma

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  4. Y

    Maximum distance an object travels when released by a spring force.

    1. A block of mass 0.247 kg is placed on top of a light, vertical spring of force constant 5 050 N/m and pushed downward so that the spring is compressed by 0.109 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of...
  5. N

    Determine the Maximum Tensile and Compressive Stresses in the Beam

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  6. S

    Principal Stress and Maximum Shear Stress

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  7. B

    Maximum possible force between two electrically charged plates?

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  8. C

    Max Wavelength of Sodium Ionization

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  9. S

    Maximum possible current in a Conductor

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  10. D

    Heisenberg Uncertainty Maximum Lifetime of Photon

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  11. A

    Why do gradient show rate of maximum increase ?

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  12. K

    Finding maximum bending moment when shear force equation is known

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  13. fsonnichsen

    Maximum Fluorescence Energy vs Excitation

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  14. Sneakatone

    Max Speed for 5142857 N Weight: Calculate Here

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  15. Sneakatone

    At what point does the jumper attain maximum acceleration?

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  16. K

    Calculating the maximum bending moment on a bridge

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  17. A

    Maximum magnetic force produced by ferrous material

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  18. R

    Maximum safe voltage for light bulb

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  19. Saitama

    Maximize Value: Solving for Largest Possible Value Using Factoring Method

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  20. D

    Working out maximum stress and Factor of safety

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  21. A

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  22. C

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  23. B

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  24. I

    Maximum Charge in an LC circuit.

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  25. T

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  26. I

    MHB A proof about maximum point, critical point and differentiation

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  27. F

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  28. 5

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  29. P

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  30. N

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  31. tsuwal

    Find the point where the eletrostatic force is maximum. (With drawing)

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  32. G

    Engineering Electrical Circuit Question - Maximum Power Dispated in Resistor

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  33. L

    What is the maximum instantaneous power that the resistance must withs

    1. A hair dryer has a power rating of 1700 W at 110 V rms. Assume the hair dryer circuit contains only resistance. 2. The peak voltage is sqrt2 * rms voltage. 3. I got my esistance of the heating element is 7.12ohm and the rms current drawn by the hair dryer is 15.45A. But I am...
  34. G

    Maximum Charge on Designed Capacitor

    I'll spare you all the details, but suppose for some reason (too complicated to get into here) I needed to design a capacitor with certain fixed parameters and only one adjustable aspect, and I wanted the design to maximize the total charge the device could store. According to my calculations...
  35. L

    Using differentiation to find maximum length problems

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  36. Sneakatone

    I on finding seconds from maximum height.

    A human cannonball was fired from a cannon with a muzzle velocity of 107 km/h. The firing angle was 45 degrees from the horizontal Ive converted 107 km/h to 29.71 m/s 1.How many seconds did it take for the human cannonball to reach maximum height? 2.How high did he rise? h =...
  37. Y

    MLE Homework: Distance Measurement with Odometer Error

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  38. 6

    What is the maximum load of an odd shaped beam with a hollow u shaped fitting?

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  39. T

    Heat pump COP theoretical maximum

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  40. A

    Maximum thermal cycle range to avoid onset of plasticity

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  41. T

    Finding the maximum value of x in a differential equation.

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  42. E

    Two reacting nuclei, maximum distance to overcome the coulomb barrier

    Basically I'm trying to find out how to find the maximum distance between two deuterium nuclei in order to overcome the coulomb barrier, causing them to fuse. Thanks
  43. L

    Which runner has a larger maximum speed?

    Homework Statement Suppose that two runners run a 100-meter dash, but the first runner reaches maximum speed more quickly than the second runner. Both runners maintain constant speed once they have reached their maximum speed and cross the finish line at the same time. Which runner has the...
  44. C

    What is the Maximum Altitude?

    Homework Statement A rocket, initially at rest, is fired vertically with an upward aceleration of 10m/s². At an altitude of .50 km, the engine of the rocket cuts off. What is the maximum altitude it achieves?Homework Equations V² = V_o² + 2aΔx t = (V-V_o)/a The Attempt at a Solution Well I...
  45. M

    Calculating Maximum Bending Stress of a Beam

    A uniform simply supported beam, 5 m long and having a cross-section as shown, is to support a load which varies linearly from zero at the left hand support to a magnitude of 20 kN/m at the right hand support. Determine the position and magnitude of the maximum bending stress. ANS : 140 MPa...
  46. A

    Calculate the tensile stress anpplied at maximum load

    (a) The steel cable to the hoist is 15m in length and has a diameter of 25mm. Its steel has a maximum permissible working stress of 200N/mm2 and a Young’s modulus of elasticity of 210,000N/mm2. The maximum load allowed on the hoist is 75kN. Determine the following:- (i) the cross-sectional...
  47. M

    Finding maximum allowable alternating stress using goodmans relation

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  48. P

    Maximum power delivered by a solar cell to a resistive load

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  49. E

    Maximum Stress on a Beam: Solving Homework Question 2 with the M/I Formula

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  50. B

    Finding elongation of bar and maximum tensile stress

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