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. K

    Calculating Maximum Force Acting on 28kg Mass: F=ma

    The position of a mass m = 28.0 kg is given in by x(t) = 3.0sin ((15.0)t). Calculate the magnitude of the maximum force acting on the mass. F=ma. I tried deriving x(t) twice to get the acceleration equation so i could plug it into F=ma and then pick a random number for t. I chose t=1 but i...
  2. Saitama

    Max Value of a_n: Find n for Maximum Value

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  3. B

    Acceleration and maximum range

    How do you calculate the acceleration and the maximum range of a jump (in this case a frog,) when the maximum vertical hight is 0.28m and the distance of acceleration is 0.086 m? I also tried to use the 45 degree, and the gravitation constant 9,81 m/s^2 but can't get it right..
  4. J

    Maximum number of path for simple acyclic directed graph with start and end node

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  5. T

    Car on a banket - maximum speed formula derivation

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  6. L

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  7. L

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  8. U

    Maximum value of F - SIN Waterloo Contest

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  9. S

    Find the maximum tension allowed.

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  10. H

    Maximum Extension of a Hanging Spring

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  11. D

    How Is Maximum Kinetic Energy Calculated for an Object on a Circular Path?

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  12. P

    F''(x)>0 in [a,b] so f has a maximum at a or b.

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  13. B

    Maximum population for 2000 Kcal per day

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  14. M

    Max Temperature: What's the Limit?

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  15. C

    Weightless Vacuum Container maximum height

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  16. W

    Find magnetic field strength and maximum force

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  17. mrspeedybob

    The maximum theoretical efficiency of a heat engine

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  18. W

    Maximum spring compression problem

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  19. B

    Drag force and maximum velocity

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  20. P

    Maximum horizontal force F on ramp with friction?

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  21. I

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    Homework Statement The problem states to find the maximum acceleration and velocity, the accleration and velocity when the displacement (x) is 1.00cm, and the equation of motion as a function of time if the displacement is A (amplitude) at t=0. We're given that the period (T) is 0.500s and...
  22. D

    How to Calculate the maximum transvers accleration and velocity

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  23. O

    Water at 4 degree Celcius has maximum density

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  24. T

    Maximum Energy Stored in a Capacitor in an AC circuit

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  25. Z

    Problem: Determine the maximum value of the average normal stress

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  26. A

    Need help deriving the general maximum height equation

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  27. L

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  28. N

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  29. P

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  30. 9

    What is the Maximum Height of a Pendulum with Given Initial Conditions?

    I'm trying to solve this problem via Lagrangian mechanics, but I'm having trouble correctly formulating the problem, I'm hoping one of you kindly people can show me where I'm going wrong. A pendulum bob of mass m hangs in the equilibrium position from a light, inextensible string of length l...
  31. AntSC

    Optics Problem - Maximum Dipole Emission

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  32. S

    Solving Max Acceleration for Physics 1 Mid-Semester

    Helping a friend out with some physics 1 mid-semester and It's been a little since I have had a physics course... so the question is "If a 30 g bird lands on a slender branch where it oscillates up and down with simple harmonic motion of amplitude 3.00 x 10^-2m and period 1.2 s"... trying...
  33. X

    Polarized light; maximum number of disagreements?

    Polarized light and their disagreements Starting with 2 vertical photons, how can we argue that the maximum number of disagreements and minimum number for +30° and -30° is Nmin(-30°,30°) ≤ N(60°,0°) ≤ Nmax(-30°,30°)? and should we also not rotate the light?
  34. P

    Is There A Maximum Possible Photon Energy?

    Ok, so I just had a thought. A Planck length is 1.63e-35m Would that mean that the smallest possible wavelenth of light is 1.63e-35m? Giving a frequency of 1.84e+43 Hz, and, of course, an energy of 3e8 J.
  35. T

    MHB Maximum value of a Quadratic Equation

    Prove that 12x-8-3x^2 can never be greater than 4. How do you prove? Do you find he discriminant? But isn't discriminant for roots only not equations?
  36. C

    Ultimate Energy: Exploring the Limits of Mass and Speed in the Universe

    New to this and was thinking about extreme cases to help me get my head around how this all works...need help.. Imagine we have an object with mass moving along. Not that this is possible, but what if all other mass in universe was somehow utilized in some nuclear reaction so ALL energy in...
  37. S

    Maximum stress in beams with different cross sections

    Homework Statement Here is the problem: I have to calculate the maximum stress for A, B and C. Homework Equations I used: σ = y*F*L / 4*I (but I don't think this is right) σ = maximum stress y = Perpendicular distance from to neutral axis F = load L = length of beam I...
  38. M

    Inverting Amplifier maximum output voltage

    Homework Statement I'm doing a physics lab that involves an inverting amplifier. I'm pretty crap when it comes to electronics. I've discovered that the output voltage won't go past 8Vrms. The amplifier is like the one here...
  39. A

    Maximum temperature under radiation

    Hello everyone, As you all know, the temperature of a metal increases under electromagnetic radiation. The metal also has a black body radiation which decreases its temperature. There is an equilibrium temperature which is the maximum temperature of the metal under the radiation. I am looking...
  40. P

    Maximum elastic energy in rope

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  41. S

    Maximum Likelihood Estimator + Prior

    1.Suppose that X~B(1,∏). We sample n times and find n1 ones and n2=n-n1zeros a) What is ML estimator of ∏? b) What is the ML estimator of ∏ given 1/2≤∏≤1? c) What is the probability ∏ is greater than 1/2? d) Find the Bayesian estimator of ∏ under quadratic loss with this prior 2. The attempt at...
  42. J

    How Do I Find the Peak Magnitude of H(jω) in a Circuit?

    Hey guys. I'm doing some homework for my circuits class and was wondering if anyone could help me with this question. How do I determine the value of ω will the magnitude of H(jω) be maximum?? In my case, the magnitude of the transfer function is (R/L)/ [sqrt((R+RI)/L)2 + ω2)]
  43. P

    Determining Maximum Wavelength of Incident Radiation

    Homework Statement When a certain metallic surface is illuminated with electromagnetic radiation of wavelength λ max kinetic energy of photoelectrons is 40.5 eV. On same surface infrared radiation of 3λ, the ma kinetic energy is 5% less than that of incident radiation. Determine the maximum...
  44. U

    Maximizing (ab+bc+ca) with a+2b+c=4

    Homework Statement Let a,b,c be real numbers such that a+2b+c=4. Then the max value of (ab+bc+ca) is Homework Equations The Attempt at a Solution I am trying to substitute for b into the second expression but that won't give me the answer. Any help would be appreciated.
  45. B

    Fluids - maximum error - diameters

    1. Homework Statement : The expressions you obtained for acceleration and drainage time (equations 3 and 4 in the manual) both contain the following factor or something equivalent: (D/d)^4-1 In the lab, we will be dealing with a bottle with a diameter around 9 cm. A typical diameter of the...
  46. P

    Maximum current a superconductor can carry

    Homework Statement Niobium metal becomes a superconductor when cooled below 9 K. Its superconductivity is destroyed when the magnetic field inside the superconductor exceeds 0.100 T. Determine the maximum current a 3.00-mm-diameter niobium wire can carry and remain fully superconducting, in...
  47. S

    How to Find Maximum Likelihood Estimators for Sample Data?

    Homework Equations L(x,p) = \prod_{i=1}^npdf l= \sum_{i=1}^nlog(pdf) Then solve \frac{dl}{dp}=0 for p (parameter we are seeking to estimate) The Attempt at a Solution I know how to do this when we are given a pdf, but I'm confused how to do this when we have a sample.
  48. S

    Maximum area between two curves within a given interval

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  49. J

    A gas in a mini universe reaches maximum entropy

    Assuming a mini-universe with the same laws as our current one. A gas within that universe reaches a state of maximum entropy. Would it remain in that state of maximum entropy once it is reached? Maybe the question does not make much sense. In that case, forgive my ignorance. edit: the...
  50. M

    Maximum Velocity of a Con-Rod with Off-set Crank.

    How do you calculate the Maximum Anglular Velocity (and angle at which this occurs) of a connecting rod which uses a slider-mechanism with an offset crank? ω = 300 rpm, 10\pi rad s-1 crank shaft, r = 50mm (0 → A) connection rod, l = 200mm (A → B) When crank angle = 45 degrees, the...
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