Minimum Definition and 1000 Threads

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

    Minimum strength of pipe for load bearing

    Hello, I am working on a project and I came across a question that is a little beyond my skill set. I am designing a support for a roof, and I have the force into the post, the length of the post and I need to determine what pipe I need, size, schedule diamter, etc. How do I go about this...
  2. A

    Principal Virtual Work vs Principal of Minimum Potential Energy

    Hello Just had a quick question for a structures class. When attempting a problem, what's the main difference between applying PVW and PMPE? What would classify a problem in using one over the other? Thanks
  3. J

    Dynamics: Minimum Force Problem

    Hi, nice to meet everybody here at physicsforums.com! I'm JM92 and I have a physics problem I need help with. Homework Statement Find the smallest value of the mass M for which the system will remain at rest given that the coefficient of static friction is 0.100...
  4. D

    Minimum force necessary to push out a cork

    Homework Statement 2 arms of a u-tube are not identical, one having twice the diameter of the other. a cork in the narrow arm requires a force of 16n to remove it. the tube is filled with water and the wide arm is fitted with a piston. the min force that must be applied to the piston to push...
  5. M

    Minimum Surface Charge Density for Spark Creation

    Homework Statement A spark occurs at the tip of a metal needle if the electric field strength exceeds 3.0x10^6 N/C. What is the minimum surface charge density for producing a spark? Homework Equations int(EdA) = (Qin) / e0 The Attempt at a Solution I imagine the surface as a cylinder with...
  6. S

    Minimum energy and power, break-even; inertial fusion

    Homework Statement A small 50:50 D-T pellet of density p=3g/cm^3 is used for inertial fusion. Estimate minimum energy and power of the laser device required to heat the pellet to T=10^4 eV and to achieve the energy break-even condition Homework Equations Lawson criteria: nt>10^20...
  7. K

    Geometric proof: minimum angle to point in a line segment

    Hi, I have a problem I need to solve for a piece of software I'm writing, and I think I've got it but it would be great if somebody could take a quick look at this proof and see if I've overlooked anything. Thanks in advance. Here is the problem: We're working in R_3 here. Given a line...
  8. C

    What Is the Correct Minimum Velocity from Infinity?

    Homework Statement <In Pic 1> Homework Equations (1/2)mv2 = ΔU The Attempt at a Solution I thought that if i apply the equations i'll have my answer but i got 2.5m/s while answer is 3m/s Please refer the solution given by some book --- Pic2, Pic3 <sorry for bad image, my...
  9. D

    Minimum finite distance in Di-hydrogen

    A simplest example of a chemical bond is that formed by two hydrogen atoms in a H2 molecule. a) Show that in the ground state (both electrons in the bonding orbital), the molecular energy has a minimum at a finite distance r=.074nm, defining the bond length for H2. b) Determine the energy...
  10. S

    Minimum degree of polynomial time NP complete problem algorithm

    So no one is quite sure that P != NP, although they tend to favor that relation. But I was curious, has anyone proved a minimum degree order to any algorithm that solves NP complete problems in polynomial time? In other words, they don't know if it can be done in polynomial time, but do they...
  11. E

    Minimum uncertainty wave packets energy interpretation

    I am having trouble understanding (not for homework) what a wave packet is in terms of the correspondence of the idea of a wave packet to a "point like" particle. I'd like to focus on the 1d wave packet ultimately, but in order to describe my consternation -- let me detour to a well defined...
  12. Loren Booda

    Does life develop where entropy is minimum?

    Is life most likely to start near greatest statistical mechanical order? For instance, DNA's extended regular structure might relate lowest entropy for its molecular weight. Is biochemical replication the antithesis of randomness? Does the apparent rarity of life in the universe reflect the...
  13. W

    Minimum change in velocity Helpppp?

    Minimum change in velocity! Helpppp? Homework Statement Calculate the minimum change in velocity (delta V or ∆V) required for the Space Shuttle to decrease its altitude to 60 miles if it’s orbiting with an apogee of 236 miles and a perigee of 215 miles above the surface of Earth. Use the...
  14. D

    What is the minimum height of the bag needed for glucose infusion?

    Homework Statement A collapsible plastic bag contains a glucose solution. If the average gauge pressure in the vein is 15000 Pa, what must be the minimum height of the bag in order to infuse glucose into the vein? Assume that the specific gravity of the solution is 1.04. The acceleration of...
  15. O

    How i find the Local minimum or Maximum Of the Function

    [(there is an option that there is no Local minimum or Maximum point in this Function) BUT i need to show the way. thanks.
  16. V

    Maximum and Minimum values of a function (2 vars)

    Homework Statement Find the max and min values of the function f(x, y) = (x-y)/(2 +x2 + y2) over the disk x2 + y2 <= 4 Homework Equations The Attempt at a Solution fx = 1/(2 +x2 + y2) + -2x(x-y)/(2 +x2 + y2)2 = (2- x2 + y2 +2xy)/(2 +x2 + y2)2 Should equal zero when x=1 y=...
  17. D

    Minimizing a function with a minimum constraint

    Minimizing a function with a minimum constraint... Homework Statement A firm would like to produce q units of output at the lowest cost. It's cost structure is rk + wL. Minimize this function with respect to the constraint: min {sk, L/S} = q K = represents capital l = represents labor...
  18. A

    Optimization ( Applied Max and Minimum )

    Homework Statement From a square piece of cardboard, 30 cm on each side, an open topped box is to be constructed by cutting the squares from the corners and turning up the sides. What are the dimensions of the box of largest volume? The Attempt at a Solution I know how to do...
  19. S

    Calculating the Minimum Safe Drop Height for a Bungee Jumper

    Homework Statement Our lab was to predict the distance a bungee jumper will fall before coming to rest. I already found the spring constant When we have the spring constant we had to find the minimum safe drop height for a bungee jumper before being stopped by the spring. The following...
  20. L

    How to derive minimum radius ratio for a given coordination number

    Homework Statement Calculate the minimum radius ratio for CN = 3. Givens: Minimum radius ratio for CN = 4 is 0.225, so that's also the max for CN = 3. The Attempt at a Solution I know that the radius ratio determines the CN, which is related to the geometry, and that for a CN of 3, the...
  21. F

    Solving for Minimum Velocity: Ball & Rock

    Homework Statement As in the attachement, find the minimum v such that the ball does not touch the rock. The Attempt at a Solution The solution given is mg*cos(theta) - mv^2/R = n < 0, where theta is the angle between the ball and the person. My question is why is there a normal...
  22. H

    Proving the Minimum of a Summation: Solving for f(x) with n Odd and Even Cases

    Homework Statement of f(x) = \sum | x - a_i | ( i = 1 to n ) where a_1 < a_2 < ... < a_n The Attempt at a Solution I believe I have proven that if n is odd then the minimum is as ceiling a_(n/2) or a_(n+1)/2. The book says a_(n-1)/2 though, but I think it's wrong.. if...
  23. G

    Optimizing Work: Finding the Minimum Path in Non-Conservative Vector Fields

    I was wondering, if you have a non-conservative vector field (so that the line integral of each path from point A to point B isn't the same) that represents some sort of force, then is there a method to find the path that requires the least amount of work from a designated point A to point B...
  24. A

    Resolving Power and minimum seperation

    (a) Two stars are photographed utilizing a telescope with a circular aperture of diameter of 2.42 m and light with a wavelength of 547 nm. If both stars are 1022 m from us, what is their minimum separation so that we can recognize them as two stars (instead of just one)? theta=1.22*...
  25. B

    Calculating Total Height of Cylinder with Two Identical Cones on Each End

    a cylinder has two identical cones one each end. the volume of the object is 50(pie/3) find the total height. so 2h+k=height. where to from there
  26. W

    Graphs to find minimum days for meetings

    Homework Statement Nine students A, B,..., I serve as members on eight committees, as follows. Committee 1: A, B, C, D Committee 2: A, C, D, E Committee 3: B, D, F, G Committee 4: C, F, G, H Committee 5: A, H Committee 6: H, I Committee 7: G, H Committee 8: E, I Each committee is to meet...
  27. M

    Help:Finding the minimum force to restain a block

    Using basic statics determine the minimum load required on a rock anchor to restrain a cube with a volume of 30 m3 if it were resting on a discontinuity with an angle of 60 degrees. The Attempt at a Solution the cube in question is meant to be a cube of granite. it has a density of 2700...
  28. P

    Maximum entropy and minimum energy principles.

    I'm looking for precise formulation of maximum entropy (second law of thermodynamics) and minimum energy principles. For example the following formulation of the second law (maximum entropy principle) which can be found in Callen's Thermodynamic book is quite good: There exists a function...
  29. M

    Maximum and Minimum : Langrange multiplier problem

    Homework Statement Find the maximum and minimum of the function f over the closed and bounded set S. Use langrange multiplier method to find the values of the boundary points. Homework Equations f(x,y) = (1+x+y)2 S = {(x,y) : x2/4 + y2/16 <= 1} The Attempt at a Solution...
  30. S

    Repulsive central force, finding the minimum separation distance

    Homework Statement A particle of mass m is subject to a repulsive central force Am/r^{3} (A is a constant). At a large distance from the center of force, the particle has speed v_{0} and its impact parameter is b. Use conservation of energy and angular momentum to show that the closest m comes...
  31. V

    Partial Derivatives Maximum and Minimum Values

    Homework Statement Find the absolute maximum and minimum values of f on the set D. f(x,y) = 1+4x-5y D is the closed triangular region with vertices (0,0) (2,0) (0,3) Homework Equations To find the absolute maximum and minimum values of a continuous function on a closed, bounded set : 1. Find...
  32. I

    Minimum speed at the circular track

    Homework Statement What is the minimum speed of the car must have at the top of the loop? There are three methods. I would like to know which method or answer is correct. Please see attached file. Homework Equations Please see attached file. The Attempt at a Solution Please...
  33. B

    Minimum area between f(x) and a tangent line

    How would you write a proof that proves that the minimum area between a function and its tangent line is the tangent line evaluated at point p, where p is the midpoint on a given interval? i.e. The minimum area between x^2, and its tangent line on the interval [0,1]...
  34. Z

    What Are the Maximum and Minimum Voltages Generated by a Generator?

    Homework Statement Hi there, motor and generator gurus Suppose a generator has the following specifications, and the rotor turns with frequency 10 Hz. Determine the maximum and minimum value of the voltage generated, using the formula: ε = Βlv n = 1000 loops = 1000 B = 10 Tesla I...
  35. R

    Is Min Function a Valid Metric on Cartesian Product Spaces?

    Homework Statement Let (X, d1) and (Y,d2) be metric space. Define a function d:(X x Y)x(X x Y) to R by d((x1,y,1), (x2,y2))=min{d(x1,x2),d(y1,y2)}. Is d a metric on X x Y? Explain Homework Equations N/A The Attempt at a Solution Is it enough to say that the min for...
  36. nomadreid

    T-symmetry (string theory) for minimum length?

    If I understand Brian Greene’s argument (in The Elegant Universe, and repeated elsewhere) for the Planck length being the minimum measurable length based on T-symmetry in string theory, it goes something like this: There are two ways to measure things, one with vibrational energy v and one...
  37. J

    What is the minimum energy of a compton scattered photon?

    Homework Statement 662 keV photons are emitted as a result of the decay of Cesium 137. These photons undergo Compton scattering. What is the minimum energy of a Compton scattered photon? What is the maximum Compton electron energy? What is the range (cm) in tissue of a Compton electron that...
  38. Char. Limit

    Finding the Closest Point on a Plane to a Given Point

    Homework Statement Find the point on the plane x-y+z=4 closest to the point (1,2,3). d=\frac{2}{\sqrt{3}} Homework Equations Hmm... The Attempt at a Solution As you can see, I've already solved for the shortest distance. But, knowing the plane I'm on and the distance, how do I...
  39. Z

    Finding minimum value of force P given static friction

    Homework Statement A crate of weight Fg is pushed by a force P on a horizontal floor. (a) If the coefficient of static friction is us and P is directed at angle theta below the horizontal, show that the minimum value of P that will move the crate is given by P = ( us*Fg*sec(theta)) / (1...
  40. L

    Angle Of Minimum Deviation (Prism & Spectrometer)

    Homework Statement Hello, one of the things I have to do for my lab report for this week is to prove that the angle between the left and right deviations of the telescope is twice the angle of minimum deviation. Its a lab where you have to find the refractive index of substances using a...
  41. Q

    Find Magnitude of Force F3 for Min Resultant FR

    Homework Statement Suppose we have the following forces: F1=[5i]kN F2=[-4j]kN F3= unknown force 30 degrees from + y-axis. How do you determine the magnitude of F3 such that the resultant FR for all three forces is a minimum? Thanks in advance.
  42. G

    What is the minimum radius of curvature of the curve?

    Homework Statement A civil engineer is asked to design a curved section of roadway that meets the following conditions: With ice on the road, when the coefficient of static friction between the road and rubber is 0.1, a car at rest must not slide into the ditch and a car traveling less...
  43. F

    Uncertainty relation: minimum value

    Homework Statement Show that the smallest possible uncertainty in the position of an electron whose speed is given by \beta = v/c is \Delta x_{min} = \frac{h}{4 \pi m_0 c}\sqrt{1-\beta^2} The Attempt at a Solution Since \Delta x \Delta p \geq \frac{\hbar}{2} , we see that \Delta x_{min}...
  44. H

    Minimum distance in which the car will stop?

    Homework Statement A car is traveling at 51.0 mi/h on a horizontal highway. If the coefficient of static friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop?Homework Equations \Sigma \vec{F} = m \vec{a}...
  45. B

    Minimum Work Input/Power Required to Freeze 50kg Water & Heat a House

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  46. H

    What Are the Optimal Kicking Angles for a Field Goal in Football?

    Homework Statement a football kicker can give the ball an initial speed of 25m/s. what are the least and greatest elevation angles at which he can kick the ball to score a field goal from a point 50m in font of the goalposts whose horizontal bar is 3.44 m above the ground. Homework...
  47. P

    Finding minimum V and angle given horizontal and vertical travel

    Homework Statement a mountain climber plans to jump from A to B over a crevasse. Determine the smallest value of the climbers initial velocity Vo and the corresponding value of the angle alpha so he lands at B Homework Equations A to B is 1.8m horizontal distance and B is lower than A...
  48. U

    Minimum Force to Make an Object Move

    Homework Statement A 6 kg object sits on a horizontal surface with coefficient of friction = .8. What is the minimum force (not necessarily horizontal) necessary to make the object slide? Homework Equations Fsmax = u * Fn where Fsmax is the force that must be overcome to make an object move, u...
  49. C

    Thermodynaics, solving for minimum power to heat water

    An electric hot water heater takes in cold water at 15.8°C and delivers hot water. The hot water has a constant temperature of 45.6°C, when the "hot" faucet is left open all the time and the volume flow rate is 5.0 multiplied by 10-6 m3/s. What is the minimum power rating of the hot water...
  50. B

    Calculating Minimum Required Velocity

    This is a tough question. I'd like to know if anybody can find a good solution. It isn't required for any of my classes, but I'd like to see a theoretical result. It seems like it should be a simple projectile motion problem, but it's not that easy. Let's say there's a building x1 meters away...
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