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. V

    Minimum beam dimension for specific max stress

    Homework Statement A beam (note: part of a truss, I chose to use the beam in the truss with the most force and length for my calculations, which I assume is the correct thing to do) of length 6m with a force of 9N is being constructed out of a material with a Young's Modulus of E = 70 \times...
  2. L

    Atomic Energy Levels - Calculating the Minimum Energy of Light Emitted

    Homework Statement Determine the longest wavelength of light emitted from this atom. Homework Equations \lambda=\frac{hc}{E} The Attempt at a Solution I calculated the lowest energy of the light emitted: E_{min}=2.1(eV) Then the longest wavelength would be...
  3. A

    Using uncertainty principle to find minimum Kinetic Energy expectation value

    Homework Statement Assume that a particle travels with a certain known (average) velocity ##v = \left\langle\hat{p}/m\right\rangle##. You know it's position with an uncertainty ##Δx##. Use the uncertainty principle to determine the least possible value for the article's kinetic energy...
  4. S

    Circular motion-find the minimum speed

    The question is: A ball of a mass 4kg is attached to the end of a 1.2m long string and whirled around in a circle that describes a vertical plane..what is the minimum speed that the ball can be moving at and still maintain a circular path? i try solve it by use T+mg=mv*2/r.But i can't find...
  5. N

    Maximum and minimum values of 7s complement in base 7

    Homework Statement What are the maximum and minimum values that can be represented using a 7s complement representation in base 7, using a 5 digit number? Homework Equations The Attempt at a Solution Would you divide the numbers so that any number starting with an odd digit is...
  6. F

    Minimum force needed to move block

    This isn't a specific problem, but it is a concept that appears in several problems. I'll give an example problem that should make clear what I mean. A block rests on a horizontal surface. Ffric≤1 N. What force (applied horizontally) is needed to move the block? My physics professor...
  7. P

    Mechanics: Calculating the minimum height for a bullet to launch from to hit a target

    1. The muzzle speed for a Lee-Enfield rifle is 630 meters per second. Suppose you fire this rifle at a target 700 meters away and at the same level as the rifle. a - In order to hit the target, you must aim the barrel at a point above the target. How many meters above the target must you aim...
  8. Spinnor

    Repeling particles on a ring, minimum angular momentum.

    Say we have two particles of mass m which repel each other, V = V(seperation). Let these particles be constrained to move on a circle of radius r. The particles want to stay at opposite sides of the circle because they repel each other. We want to treat this as a quantum problem so the particles...
  9. S

    Projectile Motion, finding minimum speed

    Homework Statement A gazelle leaps over a 2.1m fence. Assuming a 45° takeoff angle, what is the minimum speed?Homework Equations 1. x=v0x * t 2. y = v0y * t - 1/2gt2 3. vy = v0y - gt 4. vy2 = v0y2 - 2gΔyThe Attempt at a Solution I assumed at the top of the leap, vy=0 m/s, so I used equation 4...
  10. E

    Minimum Satellite Period problem

    Clever guy that I am, I am writing a small paper on Celestial Mechanics...simplified...really really simplified. However, if I bore a tunnel through the Earth and drop a watermelon through it, the watermelon returns to my hand in 76 minutes. This is an example of an elliptical orbit of e=1 But...
  11. P

    Solving for the minimum speed a car must have to catch up to another car?

    1. A blue car pulls away from a red stop-light just after it has turned green with a constant acceleration of 0.9 m/s2. A green car arrives at the position of the stop-light 4 s after the light had turned green. What is the slowest constant speed which the green car can maintain and still catch...
  12. V

    Minimum initial velocity of the projectile launched at what angle

    Homework Statement Assume there is a wall located 100m downrange (x=100) from the projectile launching position (x=0) that is 55m (y=55) high. What is the minimum initial velocity of the projectile launched at what angle necessary to clear the wall? Homework Equations h=(v^2sin^2α)/2g...
  13. C

    What the minimum mass for a habitable exoplanet or moon?

    So I've read that super Earth's masses 2-10 can be habitable hold thick atmosphere and generate plate tectonics. So I am wondering the absolute minimum mass an exoplanet or moon can be to stay habitable in the liquid H2O zone? I guess these would be called subEarth's.
  14. azizlwl

    For each real number x, let f(x) be the minimum of the numbers 4x+1,

    For each real number x, let f(x) be the minimum of the numbers 4x+1, x+2, and -2x+4. What is the maximum value of f(x)?
  15. R

    Maximum and minimum values

    i know this is a basic calculus question, but i can't seem to get two answers. G(x) = 1/2 x^2sin2x+1/2 xcos2x - 1/4 sin2x find the maximum and minimum values for G(x) on the interval [0,pi/2] i found G'(x)= x^2 cos2x and i know that there is a global max at pi/4 but i can't find the...
  16. A

    Minimum distance between a point and a geometric locus

    Hi guys I have a problem to solve, I'd like to find the minimum distance between a point and a geometric locus described in closed form, for example the intersection of two circles: p= point coordinate p1= center coordinate circle 1 p2=center coordinate circle 2 r1=radius of circle 1...
  17. D

    Minimum Distance Between Earth & Mars: Analytic Calc

    What is the minimum distance between Earth and Mars in course of their rotation in orbits? I need the derivation and analytic calculation. If we assume the plane of rotation is different for Earth and mars, the problem become to complicated. So the orbits may be assumed co-planner.Please...
  18. T

    Heat engine- calculating minimum energy per cycle from hot reservoir

    Homework Statement A heat engine operating between freezing and boling points of water takes 20 cycles to raise a mass of 1000kg through a height of 3m. Calculate the minimum energy per cycle that must be extracted from the hot reservoir in order to achieve this. Homework Equations...
  19. X

    Find minimum velocity of emitted electron

    Homework Statement Photoelectric experiment show that about 5eV of energy are required to remove an electron from platinum, if light of 150nm wavelength is used, what is the velocity of the emitted electron?Homework Equations de broglie's equation, E=hvThe Attempt at a Solution Tried by using...
  20. X

    Finding approx. minimum value for 'v'

    Homework Statement A 2m wide truck is moving with a uniform speed v=8m/s along a straight horizontal road a pedestrian starts to cross the road with a uniform speed u when the truck is 4m away from him minium value of v? Homework Equations The equations of motion in a straight line, and...
  21. D

    Minimum variance unbiased estimator

    Homework Statement Let \bar{X}1 and \bar{X}2 be the means of two independent samples of sizes n and 2n from an infinite population that has mean μ and variance σ^2 > 0. For what value of w is w\bar{X}1 + (1 - w)\bar{X}2 the minimum variance unbiased estimator of μ? (a) 0 (b) 1/3 (c) 1/2 (d) 2/3...
  22. B

    Minimum volume for filling bottles

    Your first assignment at El Smello Perfume Co. is to determine the proper setting for filling the bottles. The company wishes to keep profits high by using as little perfume as possible, but a government regulation states that no more than 2.5% of the bottles may contain less than the stated...
  23. C

    How do I calculate the minimum torque needed for a grinder motor

    I'm working as an intern trying to automate this grinder system. I would like to find the minimum torque needed for the grinder motor. The grinder motors we currently use have: 1.25 HP RPM between 8,000-11,000 13 amps 120 volt AC The grinded surface has a: Coefficient of Friction...
  24. C

    MHB Minimum area of an odd number-sided, equilateral polygon with side lengths of 1 unit.

    Suppose you look at all of the equilateral (non-self-intersecting) polygons** with an odd number of sides, and each side length is equal to 1 unit. For examples, the polygon with the fewest number of sides in this group is the equilateral triangle, and then the next one is an equilateral...
  25. X

    Schools Minimum GPA to transfer from Community to a decent 4 year college.

    I have a friend who will be starting CC in the fall and he wants to transfer to a four year college eventually. I've been telling him that he'll need a 3.0 GPA and above to transfer and this scares him. I'm doubting my own words about a 3.0. What would you guys think is usually the minimum GPA...
  26. J

    Glass that has minimum reflection and absorption at 1550nm

    I am building an enclosure for my laser that emits at 1550nm. I need to integrate a window for the laser light to pass through. Anybody have any recommendations on what kind of glass would work best so that the optical losses are kept at a minimum? Ideally, it would be commercially available...
  27. H

    2-stage rocket - minimum mass necessary

    Homework Statement I have to design a two-stage rocket to accelerate a payload of 100kg from rest to a final velocity of 6,000 m/s (no gravity to worry about) using the minimum amount of mass for the rocket stages. Each stage of the rocket must obey the following restriction: Whatever...
  28. H

    Priniciple of Minimum Energy vs. Maxwell equations

    Dear all, I'm studying a paper on coupled magneto-mechanical problems. Suppose we have a "deformable" ferromagnetic bar placed in an initially uniform magnetic field. Both ends of the bar are clamped. The bar has magnetostriction property, so it may expand or contract depending on the the...
  29. T

    Multivariable Calculus: Finding the minimum and maximum value

    Homework Statement Given f(x,y) = xy(x+2y-6), let D be the region in the plane between the hyperbola xy = 4 (let this be g) and the line x+2y-6 = 0 (let this be h). Find the maximum and minimum values of f(x,y) on D. The Attempt at a Solution I first found the critical points for f(x,y)...
  30. A

    How to calculate the minimum pipe wall thickness in this scenario

    Hey guys, Hope you can help me with the following practical problem I am facing right now. I plan to build a pipe system in which ethanol (vapor/liquid) is being conducted at pressures from 1 atm to 10^(-2) atm. What would the minimum pipe wall thickness be if the pipe material was a)...
  31. J

    MHB What is the minimum value of a trigonometric expression with a given condition?

    If $A+B+C=\pi$. Then Minimum value of $\cot^2(A)+\cot^2(B)+\cos^2(C)$ is
  32. M

    Trying to design a gear with minimum thickness

    Hello, I am blanking on the equations I should use to calculate the stress through a section of a gear. I would like to be able to calculate the thickness of trepanned gear. Hopefully the attachment helps show what I am looking for. The area between the arrows needs to be minimized...
  33. T

    Can linear algebra convert the minimum column vector in a matrix?

    I'm doing a particular form of regression that gives a eigenvector and matrix for the solution. I'm using two matrix libraries to code the solution. One library yields the minimum column vector in each column. The other does not, is there a method in linear algebra to convert the eigenmatrix...
  34. T

    What's the Minimum Energy of a Wave Needed to View a 0.1 nm Particle?

    I have a problem that ask for the minimum energy of a wave that we will use to see a particle of size .1 nm. I understand that I can not see a .1 nm particle with any wave length larger than .1 nm. I thought this would be easy and I would use De Broglis relation of electron waves. (f=E/h) or...
  35. T

    Finding the minimum and maximum distances using Lagrange Multipliers

    Homework Statement What I don't understand is why you can maximize the distances squared - d2. Isn't d2 different from d? I don't see how they can get you the same value.
  36. C

    Minimum Distance between surface of sphere and cube

    Homework Statement Find the minimum distance between the surface of a sphere with radius 3 with center (2,1,2) and a cube with length 6 with center (12,11,12) Homework Equations sphere formula: (x-x0)^2+(y-y0)^2+(z-z0)^2=r^2 The Attempt at a Solution Don't know how to attempt this...
  37. N

    Maximum and Minimum EMF in a generator

    Just a quick question, if the maximum induced EMF of a generator is say 200v, would the minimum EMF be -200v or 0v? No equations necessary I say.
  38. D

    Heisenberg Uncertainty Principle - find minimum uncertainty in position

    Homework Statement Assume speed of 435g football is known with 1mm/s uncertainty. What is the minimum uncertainty in its position? Homework Equations I'm not quite sure... I know p=mv, and I know that Heisenberg's uncertainty principle states that certain parameters of quantum...
  39. K

    Minimum distance/energy bird flight problem.

    Minimum distance/energy bird flight problem. (SOLVED) SOLVED: Problem was just a simple arithmetic error (14 squared) Homework Statement A bird is released from point A on an island 5 mi from the nearest point B on a straight shoreline. The bird flies to a point C on the shoreline and...
  40. M

    Maximum and minimum of f(x,y) within a confined domain

    Homework Statement f(x,y)=2x3-2y3-3x2 K={(x,y)\inℝ2:x2+y2≤5,y≤0} Find the maximum and minum of f(x,y) within K. Homework Equations ∇f(x,y)=(6x2-6x,-6y) Hess(f)=diag(12x-6,-6) (relevant?) The Attempt at a Solution What I've done so far was calculate the pair(s) (x,y)...
  41. Spinnor

    Changing the orbit of a satellite, minimum rocket burns.

    Suppose we have a satellite in an elliptical orbit around the Earth with the major axis pointed towards some fixed point in the heavens. What is the minimum number of rocket burns so that the major axis is rotated 90 degrees and the final and initial energy are the same. Is the number 2? At...
  42. H

    Minimum distance of a point on a line from the origin?

    Consider the graph of $${x^2 + 2 y^2 = 1}$$. What is the minimum distance of a point on the graph to the origin? When I calculated the point which has minimum distance from origin it came out to be (1,0) implying the min distance to be 1. The answer is 1/2. Help?
  43. E

    Calculate the minimum thickness

    Homework Statement I have a large polymer plate of 45cm x 120cm, with Young Modulus 0.8 GPa and I want to calculate the safe thickness (before fracture) of that plate on a middle line force across the width of the plate with magnitude of 0.6 kN. The middle line force distribution is shown...
  44. J

    Doppler Effect: Minimum Recessional Velocity for Its Effect

    Consider a stationary observer and an emitter of light radiation that may be either receding or approaching at a variety of nonrelativistic velocities, with the velocity of the emitter having only a radial component and no transverse component. I was wondering whether the Doppler Effect...
  45. T

    Double Slit Experiment - White Lite & Minimum Angular Displacement

    Homework Statement A two-component beam of light, consisting only of two wavelengths 650 nm and 520 nm, is used to obtain interference fringes in a double-slit experiment. The separation between the centers of the slits is 2.43×10−4 m and the distance of the plane of the slits from the...
  46. F

    Calculating Minimum Sampling Rate for Fourier Signal

    Hello, I have the following Fourier complex signal: v(t) = 2/πsin(500πt)+1/2sin(1000πt)+1/3sin(1500πt) I need to find the minimum sampling rate for this signal. So, according to the Nyquist Theorem, the sampling rate must be twice the highest frequency component contained in the original...
  47. J

    MHB Minimum degree of a polynomial passing through points

    If p(x) is a polynomial such that p(0)=5 ,p(1)=4 ,p(2)=9,p(3)=20 , the minimum degree it can have
  48. J

    MHB Finding the Minimum Value of y

    If y = \mid x \mid+\mid x-1 \mid+\mid x-3 \mid+\mid x-6 \mid+...+\mid x-5151 \midand m = no. of terms in the expression yand n = no. of integers for which y has min. valueThen \displaystyle\frac{m+n-18}{10} =
  49. K

    The minimum cost of converting static pressure into dynamic pressure

    Can static pressure be induced to becoming dynamic pressure through the use of "right-angle forces" with respect to particle velocities? I imagine that one could accomplish this with an ionized gas and a magnetic field. This would reduce the amount of work that is need to accelerate the gas...
  50. C

    What is the minimum amount that the spring must be compressed

    Homework Statement A 0.25 kg projectile is launched across a frictionless surface by a spring of spring constant k=1200 N/m. The block is then redirected up a 25 degree incline and sent through the air with the intent of clearing a 1.2 m high wall that is 4.0 m away from the end of the...
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