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 load platform can withstand

    Homework Statement A platform is supported by a rectangular plastic tank below . When there's no external load act on it , it oscillate on the water surface with amplitude 0.05m . When it's in equilibrium , the water reaches 0.07m of the height of tank submerged in water. P/s : the tank has a...
  2. P

    What is the Maximum Height Achieved by a Soccer Ball Kicked at a 45° Angle?

    Homework Statement A soccer ball is kicked at a 45° angle. If the ball is in the air for 3 s, what is the maximum height achieved Homework Equations y=viy + 0.5 x ay x t The Attempt at a Solution i used trig to get the vertical and horizontal components i got 2.2 for each side (as there the...
  3. I

    Current at maximum power - PV cell

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  4. A

    The speed of a projectile when it reaches its maximum height

    Homework Statement The speed of a projectile when it reaches its maximum height is one-half its speed when it is at half its maxi- mum height. What is the initial projection angle of the projectile? Homework Equations Vf2 = vi2 + 2axThe Attempt at a Solution I know that the speed at the top...
  5. Q

    Finding the maximum load capacity of a shelf

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  6. G

    Maximum power factor of three phase receiver

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  7. RoboNerd

    Question on finding maximum magnitude of acceleration

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  8. I

    Calculating the maximum shear stress in a shaft

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  9. A

    What is the Maximum Speed Needed to Avoid a Collision?

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  10. JulienB

    Contraction, integral, maximum norm

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  11. Albert1

    MHB How to Find the Maximum of the Function f(x)=12x-32+24√(9-3x), for x≤3?

    $f(x)=12x-32+24\sqrt {9-3x}, x\leq 3$ find $max f(x)$
  12. JulienB

    Maximum norm and Banach fixed-point theorem

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  13. Evangeline101

    Maximum height of a spring toy

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  14. H

    Finding Maximum Number of Interference Maxima?

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  15. whatphysics

    Using differentials to estimate the maximum possible error

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  16. Monsterboy

    Maximum height over which water can be siphoned

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  17. K

    Find the maximum thermodynamic efficiency

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  18. W

    Maximum value of Von Neumann Entropy

    Homework Statement Prove that the maximum value of the Von Neumann entropy for a completely random ensemble is ##ln(N)## for some population ##N## Homework Equations ##S = -Tr(ρ~lnρ)## ##<A> = Tr(ρA)## The Attempt at a Solution Using Lagrange multipliers and extremizing S Let ##~S =...
  19. S

    Determine the absolute maximum bending stress of the beam.

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  20. I

    What is the maximum induced EMF in a rotating contour near a straight wire?

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  21. R

    Maximum acceleration of a spring

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  22. lep11

    Prove f has maximum value in R

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  23. M

    Max Photon Energy: Planck Length Lower Limit?

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  24. JulienB

    Finding Extrema of a Set: A Derivative Approach

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  25. twiz_

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  26. anemone

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  27. scotty c

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  28. R

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  29. blueray101

    The maximum deformation of the ball?

    Homework Statement Part 1: I've worked out part 1 already. The answer is 4650m/s^2 A ball travels vertically downwards until it hits a concrete floor with speed 22.7-m/s. It then bounces vertically upwards at 10.8-m/s. Examination of a high speed video shows that the collision took 7.2-ms...
  30. Jess Karakov

    Trapezoidal Rule: Maximum error in approximation?

    Homework Statement Suppose that T4 is used to approximate the ∫ from 0 to 3 of f(x)dx, where -2 ≤ f ''(x) ≤ 1 for all x. What is the maximum error in the approximation? Homework Equations |ET|≤ (K(b-a)^3)/(12n^2) The Attempt at a Solution So I know how to find the error of the trapezoidal...
  31. A

    What is the maximum charge on plates when dielectric removed

    Homework Statement A capacitor with two parallel plates of area 88.5 cm2 and nylon (dielectric strength 14 MV/m) inserted between them breaks down when a potential difference of 5.80 kV is applied. What is the maximum charge the plates will hold when the nylon is removed and the space filled...
  32. N

    Maximum Error Using Differentials

    Homework Statement 2 adjacent sides of a parallelogram measure 15ft and 10ft w/ max errors of ±0.1ft angle is 45° w/ max error of ±0.5° What is the maximum error in the calculated value of the area or the parallelogram? Homework Equations A = area = xysinθThe Attempt at a Solution x = 15ft...
  33. U

    Structural engineering question -- maximum load taken by beam

    dear all , My question is what is the maximum load taken by beam of UB 610 x 229 x 125Kg/m for a span of 5 mtr? its supported on both side by anchoring on concrete beam.
  34. M

    MHB Finding the Maximum Value of n for a Given Equation

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  35. Elena14

    Maximum kinetic energy in projectile motion

    Finding the maximum kinetic energy in a simple parabolic projectile motion requires us to find the maximum velocity. I know that the velocity will be maximum at two points, the point of projection and point of return. So there must be two points where the kinetic energy is maximum. But my...
  36. DaTario

    Maximum number of layers of immiscible of fluids

    Hi All, What is the maximum number of layers of immiscible fluids in nature. Is seems intuitive to me that this limit exists. for the sake of definiteness, let' s consider usual laboratory"s condition of temperature and pressure. Best wishes, DaTario
  37. avito009

    Is 2.5 m maximum length of lintel? Why?

    I read this in Gordon's book "Structures or why things don't fall down". I read that the maximum length of lintel should be a maximum of 2.5 metres. Why? What if its more?
  38. T

    Maximum height water can be projected onto a wall

    Homework Statement H3-1 Determine the maximum height on the wall to which the firefighter can project water from the hose if the speed of the water at the nozzle is 20 m/s. The firefighter stands 18 m away from the wall and holds the nozzle 1.2 m above the ground. Homework Equations The...
  39. L

    Binding energy/position of maximum energy value

    Homework Statement The binding energy of the ion H2+ is -16.3 eV at the equilibrium separation 0.106 nm. The Hellman-Feynman theorem states taht the force between the nuclei in a molecule can be calculated from the electrostatic repulsion between the nuclei and the electrostatic attraction of...
  40. C

    Maximum bending Moment and Maximum Shear Stress Question

    Is the maximum bending moment and maximum shear stress an absolute value? For example, when drawing out a bending moment diagram say if I get -400 kNm at one point and 300 kNm at a different point. If these values are the maximum/minimum points on my diagram would 400 kNm be considered as a...
  41. K

    Mathematica FindMaximum function in Mathematica

    I recently plotted a piecewise function: Plot[Piecewise[{{1 - Exp[-.002*t], 0 <= t < 120}, {-Exp[-.002*t] + Exp[-.002*(t - 120)], 120 <= t}}], {t, 0, 5000}, PlotRange -> {0, 0.25}] I then defined the function which I am calling q[t_] as follows: q[t_] := Piecewise[{{1 -...
  42. K

    What is the maximum distance for a receiver to pick up a 12.5-MHz signal?

    Homework Statement Points A and B are 56.0 m apart along an east-west line. At each of these points, a radio transmitter is emitting a 12.5-MHz signal horizontally. These transmitters are in phase with each other and emit their beams uniformly in a horizontal plane. A receiver is taken 0.500...
  43. K

    Maximum Torque in Dipoles (electrostatics)

    In a --specifically uniform electric field-- (I may be wrong here) my understanding is that the dipoles will result in no net dipole force (due to cancelling out) but there will actually be a net torque experienced about the center. This torque will be trying to turn the dipole so the moment, p...
  44. B

    What Is the Maximum Initial Velocity of a WW2 German U2 Rocket?

    Homework Statement A German U2 rocket from WW2 had a range of 300km, reaching a maximum height of 100km. Determine the rocket's maximum intial velocity. X component variables: di=0, df=300, a=0, time=9, vi=? Y component variables: a=-9.8, vf=0, vi=?, di=0, df=100, displacement=100, Note: For...
  45. D

    Maximum Likelihood and Fisher Information

    Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...
  46. D

    Find MLE of θ: Maximizing Likelihood fxn

    Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...
  47. L

    Maximum ratio of calcium, atp hydrolysis

    Hello, 1-The standard free energy associated to the hydrolysis of one ATP mole is -31 kJ. What would be the energy when [ATP]=5mM , [ADP]=0.5mM and [Pi]=1mM 2-Calculate the free energy required to move 1 mol of Ca2+ ions from the outside of the cell (where [Ca2+] = 10-3) to the inside (where...
  48. P

    Calculating Maximum Pressure for T6 Aluminium Cylinder

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  49. evinda

    MHB Find Max Function g: $\sqrt{10^{2016}}$

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  50. Priyadarshini

    Maximum number of no bond resonating structures

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