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. M

    What is the maximum emf induced in a rotating coil with given parameters?

    Homework Statement A 104-turn coil rotates 7.14 times per second. The coil has a cross-sectional area of 0.670 m2 and the magnetic field through the coils is 0.0720 T. What is the maximum emf induced in the coil? Homework Equations Honestly the rotating coil is throwing me off. But I...
  2. K

    Maximum Deceleration of a Bicycle

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  3. A

    Find Maximum Transverse velocity of string

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  4. G

    Maximum Likelihood Estimator Problem

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  5. M

    Using tensions to find maximum velocity

    An object is constrained by a cord to move in a circular path of radius 0.5m on a horizontal frictionless surface. The cord will break if its tension exceeds 16N. The maximum kinetic energy the object can have is: Attempt at solution: Well if tension can only be constant, then velocity is...
  6. Q

    Maximize a Function: Extrema of ρsinθ + cosθ over [0,pi/2]

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  7. A

    What is the Maximum Range of a Fired Shot from a Launcher?

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  8. S

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  9. C

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  10. B

    Finding Minimum and Maximum values.

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  11. M

    Why do completely inelastic collision have MAXIMUM energy loss?

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  12. O

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  13. P

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  14. J

    Calculating Maximum Force for C1018 Steel Shaft

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  15. A

    Maximum Power Transfer for Z = 12+24 Ohms

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  16. MarkFL

    MHB Maximize Volume w/ $100: Help w/ Math Max/Min Question

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  17. Albert1

    MHB Find the Maximum of n: $n^2 - 2112$

    $n\in N$ $n^2 - 2112 $ is a multipler of $n+10$ please find :$max(n)$
  18. M

    Minimum and maximum values of the objective quantity?

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  19. J

    Find the Maximum Charge of a Capacitor

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  20. K

    Finding the time at which the displacement is a Maximum - Calculus

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  21. J

    Calculating Maximum Force Applied to Shaft with Radial Undercut

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  22. F

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  23. R

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  24. J

    Maximum Percent Recovery in Ethanol/Water Recrystallization

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  25. 1

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  26. W

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  27. T

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  28. J

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  29. E

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  30. L

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    1. Homework Statement A 2-kg mass attached to a spring oscillates in simple harmonic motion and has a speed of 5 m/s at the equilibrium point. What is the maximum potential energy of this oscillating mass? 2. Homework Equations I know that the potential energy is: Ep = 1/2 kx2 k = mω2
  31. D

    Show extremum of the Entropy is a maximum

    Homework Statement The Entropy of a probability distribution is given by, S = -k_B \sum _{i=1}^N p(i)\ln{p(i)} I've shown that the extremum of such a function is given by, S' = k_B \ln{N} (which is a positive quantity) Now I want to show that this is a maximum by showing that S' - S...
  32. O

    Particle moves in one dimension given potential funct find maximum x

    Please delete this post.
  33. P

    Find the maximum speed of the elevato

    Homework Statement A person of mass mp stands on a scale in an elevator of mass me . The scale reads the magnitude of the force F exerted on it from above in a downward direction. Starting at rest at t=0 the elevator moves upward, coming to rest again at time t=t_0. The downward acceleration...
  34. T

    Determining the maximum number of minority electrons in semiconductor

    Homework Statement P-type silicon can be doped in the range from 5x1014 cm-3 to 1020 cm-3. Determine the maximum possible number of minority electrons in a neutral P-type region if the device area is limited to AD = 1 cm x 1 cm and the thickness of the P-type region is limited to tP=100 μm...
  35. S

    F(t) = some_integral; where does the maximum occur?

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  36. R

    Maximum range of an object projected from a height h

    Homework Statement A particle is projected with an initial speed u from a point at a height h from the horizontal plane. Find the equation for maximum range of the particle. Homework Equations R=u^2sin2θ/g H=(usinθ)^2/2g The...
  37. G

    Calculating Maximum Range of a Catapulted Rock

    Homework Statement Assuming that the rock launched by a catapult is released from ground level, show that the theoretical maximum range is: R=2Mh/m, where M = mass of counterweight m = mass of rock h = height counterweight falls Homework Equations Ep=mgh Ek=(mv^2)/2 The Attempt...
  38. D

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  39. F

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  40. D

    Max Flux Density for DC Generator Cores

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  41. C

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  42. R

    Finding out maximum from given velocity?

    Homework Statement Given that V(t) = π*cos(πt/1.6 + π/6), at which time after t = 0 s is the kinetic energy first at a maximum? The answer is 1.33 seconds. Although, when I put it in the calculator, 1.33s is at a minimum. How would you do this by hand? Step by step work would be appreciated...
  43. H

    Maximum speed for absorbing photons?

    Homework Statement A ray of photons coming from a laser with a wavelenght of 589.59nm meets a ray of sodium atoms (A=23) coming from the opposite direction. What is the maximum speed the sodium atoms can have in order to absorb photons? The Attempt at a Solution I thought about...
  44. J

    Showing that a continuous function achieves a maximum implies compact

    I've prove everything except for the fact that E is bounded below. It would appear that you would need to know something about the functions taking a minimum value as well to show this using my method, so perhaps there is another way of thinking about things to show a lower bound?
  45. K

    Line of maximum for a 2D 'surface'

    Hello, I hope this is the right section to post this question. While analysing the asymptotic value of a ratio of a bessel and a hankel function, I reduced it to something of the form [(1 + β/n)^ n * (1 + n/β)^ β] / 2^(n+β) ; n and β are integers and greater than 1 how do I show that...
  46. Albert1

    MHB Finding Maximum Value of $e$ in $a,b,c,d,e \in R$

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  47. H

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  48. siddharth23

    Maximum transmission ratio of a spur gear pair

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  49. W

    Maximum perpendicular height above an inclined plane

    Homework Statement A particle is projected from a point o with initial velocity u up a plane inclined at an angle 60° to the horizontal. The direction of projection makes an angle ∅ with the horizontal. The maximum perpendicular height is H. prove that H = u^2( sin^2(∅) ) / g Homework...
  50. B

    Maximum working shear stress and working force?

    Homework Statement The maximum shear force of a set of bolts is 1000 kN. The ultimate shear stress is 750 MPa and the safety factor is 3. The diameter of each bolt is 20 mm. a) What is the maximum working shear stress in each bolt? b) The cross sectional area of each bolt? c) The maximum...
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