What is Minimum: 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

    Minimum Coefficient of Friction

    In a classic carnival ride, patrons stand against the wall in a cylindrically shaped room. Once the room gets spinning fast enough, the floor drops from the bottom of the room! Friction between the walls of the room and the people on the ride make them the “stick” to the wall so they do not...
  2. C

    Minimum energy a proton must have to penetrate

    Minimum energy a proton must have to penetrate... Homework Statement Determine the minimum energy that a proton must have to penetrate 30 cm of tissue, the approximate thickness of the human body. Homework Equations I used R=[(E/9.29)^1.8]1.11x10^-3 but I'm not sure if this is correct...
  3. H

    Minimum veritcal distance between two graphs.

    Homework Statement Calculate the minimum vertical distance between the cubic y=x^3-x^2-4x+4 and the parabola y=-2x^2+16x-30, when x is positive. Homework Equations y=x^3-x^2-4x+4 y=-2x^2+16x-30 The Attempt at a Solution I have no idea at all how to work this out, so perhaps someone...
  4. S

    What Is the Minimum Average Speed Required to Catch the Ball?

    Homework Statement Suppose that you loft the ball with an initial speed of v = 13.5 m/s, at an angle of θ = 48.5° above the horizontal. At this instant your opponent is d = 10.0 m away from the ball. He begins moving away from you 0.350 s later, hoping to reach the ball and hit it back at...
  5. N

    What is the minimum amount of current that can be fatal at around 20KV?

    hi, i probably don't need to give you all this information, but i will anyway :) i have a flyback transformer from a TV connected to a 30V 1A power supply via a transistor from a TV (a high power line output transistor), and the signal on the base of the transistor is around 100KHZ...
  6. A

    Calculating minimum I-beam section area under load

    Homework Statement This seems to a reasonably basic question to go through but yet I seem to have a bit of a mental block on it. so any help in the right direction would be great.. An I-beam is 10mm thick on the web and flange, is 6m high and has a Young's modulus of 200 GN/m2. The design must...
  7. P

    Calculate the minimum frequency needed to start the electron

    Hi there. I am a student from Spain and I am about to join the University but I have to pass physics at High School. Here It is: The work of extracting an Eletron in a metal is 3.8 eV. Calculate the minimum frequency needed to start the electron. This is what I did. \[E = \phi + Ec\]...
  8. E

    Find the maximum and minimum dimension of a closed loop

    Dear all, Is there a method to find the maximum and minimum dimension of an irregular closed loop? This is a problem when we want to define the full-width - half maximum of a image. The level contour of this image at its half maximum can be an irregular closed loop. Any reference or...
  9. N

    Find the maximum and minimum values of:

    Homework Statement Find the maximum and minimum values of f(x)=x^4e^-x over [0,10] Homework Equations The Attempt at a Solution From what I remember is you set the f' equal to 0. And that will give you two more points to test. and then you put the 0 and 10 number into the...
  10. MTd2

    Minimum Size in spin networks/foams.

    I must put both of them because I want to have an idea of dynamics here, of scattering and of geometry at the same time. I will rewrite what I put in another thread: "Matter field is something that lives on a spin foam like electical fields on a electrical grid structure. Any possible...
  11. N

    Why Does Multiplying by 3/4 Affect the Solution in Maximizing Q=xy?

    Homework Statement 11. Maximize Q=xy, where x and y are positive numbers such that (4/3)x2 + y=16 Homework Equations The Attempt at a Solution I know how to do it. The first time I did it. I multiplied the (4/3)x^2 +y=16 by (3/4) and got x^2+y=12 and then y=12-x^2 when solving...
  12. P

    Really clueless = Minimum Mass Tension Force Question

    Homework Statement A fisherman yanks a fish straight up out of the water with an acceleration of 2m/s^2 using very light fishing line that has a "test value" of 50 pounds. the fisherman, loses the fish as the line snaps. What is the minimum mass of the fish? The answer given is...
  13. S

    Forces - finding minimum mass given coefficients of friction

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  14. N

    The distribution of the square of the minimum of two normal random variables

    Homework Statement Let X and Y be i.i.d normal random variables with mean 0 and variance (that is, N(0,1)). If Z=min(X,Y). Prove that the square of Z is a Gamma distribution and identify the parameters. My problem is that the cdf of a normal random variable has no exact form. I need the cdf...
  15. O

    Minimum Colors for an Icosahedron

    How could you mathematically solve for the minimum amount of colors needed for each face of an icosahedron or any regular polyhedron to not touch? (E.g. a tetrahedron pyramid would need four unique colors.)
  16. M

    Understanding the Minimum Test Score Requirement for Competitive Examinations

    Can anybody help me understand the solution to the problem at http://www.tutorvista.com/q/to-qualify-in-a-competitive-examination-candidates-must-score-in-the/q53911_86449 ?
  17. L

    What is the minimum pressure the human body can handle?

    ...assuming very slow adaptation is possible. How low can one go? And something else: if you're at very low pressure, water or blood would boil at RT (pressure is lower than the vapor pressure of water). Would this mean a relatively innocent cut wound would make you lose a lot of blood? The...
  18. C

    Minimum distance of functions in a metric space

    Homework Statement A metric on C[0,1] is defined by: d(f,g) = ( \int_0^1 \! (f(x) - g_t(x))^2 \, dx )^{1/2} Find t e R such that the distance between the functions f(x) = e^x - 1 and g_t(x) = t * x is minimal. Homework Equations Given above The Attempt at a Solution The first...
  19. S

    Bounds for the mean of the minimum of binomial random variables

    Dear Friends, I want to find an upper and lower bound for the expected value of the minimum of independent binomial random variables. What paper/book do you suggest for this problem? In other words, I need to find bounds for E(min(X1,X2,...,Xn)), where Xi 's are independent random variables...
  20. G

    Maximum and minimum distance (lagrange multipliers)

    Homework Statement A point lies on the plane x-y+z=0 and on the ellipsoid x^2 +\frac{y^2}{4} + \frac{z^2}{4} = 1 Find the minimum and maximum distances from the origin of this point. The Attempt at a Solution The two contraints g = x-y+z =h= x^2 +\frac{y^2}{4} +...
  21. P

    Finding the Minimum Angle for Motion on an Inclined Plane

    Homework Statement A box with mass of 45 kg is placed on a flat board. It starts moving when the board is inclined at 27 degrees. If the mass is doubled, what is the minimum angle needed so that it starts moving? Homework Equations Frictional force = mgsin\theta The Attempt at a...
  22. P

    What Dimensions Maximize the Area of a Rectangle Under y = 8 - x^3?

    What are the dimensions of the largest rectangle that can be drawn in the closed region bounded by the x- and y-axes and the graph of the function y = 8 - x3 A=lw=16 D= 2l + 2w = 2l + 16/l I started off by graphing the equation. The y-int was 8 and the x-int was 2. Thus, I established...
  23. cepheid

    Minimum black hole mass to survive fall to event horizon

    I'm having no end of trouble with this seemingly simple problem: Homework Statement What's the minimum mass of a black hole for which you could survive a fall through the event horizon without being ripped to shreds? Why would you be ripped to shreds for smaller black holes? Homework...
  24. P

    Minimum diameter fluid dynamics

    Homework Statement A fire-hose must be able to shoot water to the top of a building 35.0 m tall when aimed straight up. Water enters this hose at a steady rate of 0.500 m³.s¯¹ and shoots out of a round nozzle. (a) What is the maximum diameter that this nozzle can have? (4 marks) (b)...
  25. M

    Prove Max/Min of f(x) -> Sqrt of f(x) at x0

    Homework Statement prove: if f(x) bigger or the same as 0 on an interval I and if f(x) has a maximum value on I at x0(0 is written small beside the x), then sqrt of f(x) also has a maxsimum value at x0. Similarily for minimum values. Hint: Use the fact that sqrt of x is an increasing...
  26. P

    Calculating Minimum of PT = 16.8e0.0697t + 204e-0.356t

    Calculate the minimum of PT = 16.8e0.0697t + 204e-0.356t PT' = 0.0697 x 16.8e0.0697t + -.356 x 204e-0.356t Stationary points occur when PT'=0. Therefore: 0=0.0697 x 16.8e0.0697t + -.356 x 204e-0.356t My final answer was that t = 4.29. However, the Graphics Calculator begs to differ...
  27. G

    The minimum number of photons per second?

    Homework Statement An owl has good night vision because its eyes can detect a light intensity as small as 4.5 10-13 W/m2. What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 7.5 mm and the light has a wavelength of 503 nm...
  28. D

    Conversion for maximum and minimum pressure in South African water reticulation

    Hi The minimum pressure acceptable in South African water reticulation systems is 24m. The maximum pressure acceptable is 900 kPa. http://www.mangaung.co.za/docs/Regulations-Water-Conservation.pdf I need to write write a training manual for the waterworks department, and I need to...
  29. F

    Quantum Tunneling Minimum Energy

    Good day, everyone! Lately I faced the necessity of solving a problem from a field I know literally nothing about. So I just made an online research but without success. Any help (hints, good sources, relevant equations) would be greatly appreciated! Homework Statement Gold nucleus (Au...
  30. 8

    Minimum amount of work input to a refrigerator

    Homework Statement 600Kg of water at 25C has to be frozen into ice in an ideal refrigerator. The room temperature is 20C. What is the minimum amount of work input to the refrigerator to achieve this? ( specific heat capacity of water = 4170 J/Kg/K, latent heat of melting ice = 3.33 x10^5 J/Kg...
  31. R

    Minimum area of a triangle with fixed incircle

    Homework Statement Consider an isosceles triangles with height x and a fixed incircle of radius R. Show that the minimum area of such triangle occurs when x = 3R Homework Equations None. The Attempt at a Solution Well, I know that have to express the area of the triangle in terms...
  32. P

    Question on a Hypothetical Interaction- Minimum Energy- Bosons

    Homework Statement If there was a hypothetical interaction that occurs on, say, a scale of 10^{}-30m, where would one look for signatures of boson associated with this interaction. By that I mean what would the minimum energy be approximately where I would look for those signatures. Also...
  33. G

    Calculating the Minimum Proton Speed Near a Lead Nucleus

    1. Predict the minumum speed of a 20.0MeV proton as it passes within 1.0x10^-13 meters of a lead nucleus having 82 protons. (Note: 1eV = 1.6x10^-19 Joules) 2. How do I start off? 3. All i can think of is to get a charge for the lead nucleus by using q=ne which is the number of...
  34. O

    Minimum Uncertainty in Measuring Velocity of a Particle in X-direction.

    Homework Statement A small flat circular disc of diameter 2mm and mass 5mg is lowered vertically to rest at the centre of a flat tray of width 10mm in the x direction and 50mm in the y direction. What is the minimum uncertainty in measuring the velocity of the particle in the x direction...
  35. J

    Two sound sources and minimum sound points

    Two sound sources 4 m apart have the same frequency of 880 Hz. The sources emit energy in the form of spherical waves. An observer initially hears a minimum sound, since the sound sources are out of phase, at a distance of 15 m along the perpendicular bisectorof the line joining the two...
  36. K

    Local Minimum of x^4-9x^3+9x^2+5x-4 - Where am I Wrong?

    The question asks for local minimum of x^4-9x^3+9x^2+5x-4. The answer was x=-0.21 and 5.96. I thought 5.96 is the absolute minimum, since it gives the loweset y value on the open interval. Where am I wrong. Thanks.
  37. R

    Minimum distance between stars so we see them as two distinct stars

    Homework Statement Using a telescope with circular aperture of diameter 2.5 meters and wavelength 463 nm. The stars are 10E22 meters away from us. What does the distance between them have to be so we view them as two stars? Homework Equations angle = 1.22 x (wavelength/diameter) >...
  38. S

    Relationship between a given volume for a cylinder and the minimum surface area.

    I currently have a question that i am struggling with it is: Propose a mathematical model in the form of an equation desribing, in general terms, the relationship between a given volume for a cylindrical container and the minimum surface area of material required to make it.. i am...
  39. S

    Minimum Length for Safe 1000kg Plane Landing on 2000kg Barge

    Homework Statement 1000kg plane lands on a 2000kg barge on in a calm ocean. The only frictional force is equal to one quarter of the planes weight. What must the minimum barge length be to land safely if it hits the deck at 50m/s. Also there is no water friction/resistance. Homework...
  40. J

    Optimizing Triangle Dimensions for Circumscribing a Circle

    Homework Statement Find the dimensions of an isosceles triangle of least area that can be circumscribed about a circle of radius R. Homework Equations Let a,b, and c denote the lengths of the sides of this triangle and c=b. Then the angles opposite these sides are A, B and C...
  41. D

    Calc derivatives - Minimum total surface area in a box of V = 160 ft2

    Hi everyone! I'm new to online math forums. I wonder if anyone can give me a hand on this - it would be greatly appreciated. Thank you in advance! Dave Homework Statement If a box with a square base and an open top is to have a volume of 160 cubic feet, find the dimensions of the box having...
  42. Shackleford

    Minimum Kinetic Energy of a Proton Confined in a Uranium Nucleus

    36. A proton is confined in a uranium nucleus of radius 8 x 10^-15 m. Determine the proton's minimum kinetic energy according to the uncertainty principle if the proton is confined to a one-dimensional box that has length equal to the nuclear diameter. What's wrong with my equation and value...
  43. S

    Minimum value of the length of a line

    Homework Statement Two towns, A and B are 5 km and 7 km respectively, from a railroad line. The points C and D nearest to A and B on the line are 6 km apart. Where should a station be located to minimize the length of a new road from A to B? Homework Equations a^2+b^2 = c^2, a=0.5bh(?)...
  44. G

    Minimum force to keep a mass floating in the air

    This is bugging me and maybe someon can help me find the obvious mistake: I want to calculate the minimum power needed to keep a mass of 1 kg floating in mid air. The naive approach is this: The mass falls 5 meters in one second so to get to the original position I have to invest an...
  45. R

    Minimum deviation in a Prism -

    Homework Statement A ray of light is incident in air at an angle of 40 degrees to the normal to one face of a 60 degree glass prism. Calculate the angle through which the ray has been deviated by the time it emerges from the prism. (refractive index of glass wrt air is given as 1.50)...
  46. B

    Minimum speed of interaction of matter

    hi physicists, i have a gnawing question that could be put to rest with experiment but i lack the tools and challenged in ideas. we all know that the speed of light in vacuum is the maximum that can be attained in the universe. also light does not accelerate to that speed, it just begin to exist...
  47. S

    Finding minimum concentrations in a buffer solution

    Homework Statement "Calculate the minimum concentrations of formic acid and sodium formate that are needed to prepare 500.0 mL of a pH 3.80 buffer whose pH will not change by more than 0.10 unit if 1.00 mL of 0.100 M strong acid or strong base is added." Ka of formic acid = 1.8E-4 pKa of...
  48. 0

    Wave Length that gives minimum velocity?

    Homework Statement The velocity of a wave of length L in deep water is v = K square root of (L/C + C/L) where K and C are known positive constants. What is the length of the wave that gives the minimum velocity? Homework Equations Possibly a(t) = v'(t) = s"(t) The Attempt at a Solution I...
  49. U

    Minimum Volume of a Hom., Bare Cylindrical Reactor

    Just trying to do a problem to find the minimum volume for a homogeneous, bare cylindrical reactor, and my main question is if the radial and axial bucklings are equal to one another at min. V or if there is some other condition that would be helpful. Thanks.
  50. J

    Minimum problem involving rates and basic trig

    Homework Statement A man at point A on the shore of a circular lake of radius 1mi wants to reach the opposite point C as soon as possible. He can walk 6mi/h and row his boat 3mi/h. At what angle theta to the diameter AC should he row? The Attempt at a Solution My diagram looks like...
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