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.

View More On Wikipedia.org
Recent contents Top users
  1. S

    Finding minimum potential

    If we have a particle of mass m moving in the presence of the following potential in one dimension: V(x) = V0 [(e-2\gammax) - 2e-\gammax)] In order to find the minimum of the potential V do we take the derivative with respect to x? dV(x)/dx = 2*\gammaV0[(e-\gammax) - (e-2\gammax)]...
  2. O

    Minimum velocity for GEO orbit transfer

    Homework Statement A GEO spacecraft crosses the earth’s equatorial plane when its true anomaly is 30 deg. The eccentricity of the orbit is 0.1 and its initial inclination is 5 deg with respect to the equator. What minimum velocity increment is required to transfer this GEO to an...
  3. R

    Need help finding initial minimum speed

    Homework Statement A bale ejector consists of two variable-speed belts at the end of a baler. Its purpose is to toss bales into a trailing wagon. In loading the back of a wagon, a bale must be thrown to a position 8 feet above and 16 feet behind the ejector. Find the minimum initial speed...
  4. D

    Maximum and Minimum Problems in Exponential Functions

    I'm having a hard time with these two questions for an assignment in grade 12 advanced functions.. 1) Find the maximum and minimum values for each exponential growth or decay equation on the given interval. i) y=100(0.85)t, for 0 (less than or equal to) t (less than or equal to) 5 ii) y =...
  5. K

    Construction of minimum norm solution matrix

    Homework Statement Consider the linear system of equations Ax = b b is in the range of A Given the SVD of a random matrix A; construct a full rank matrix B for which the solution: x = B^-1*b is the minimum norm solution. Also A is rank deficient by a known value and diagonalizable...
  6. R

    Find minimum initial velocity of object

    Homework Statement Find the minimum initial velocity needed for a ball starting from the middle-top (highest point) of a semicircular mound with radius R to go over without touching the mound if the initial velocity has only a horizontal component. Homework Equations v=d/t The Attempt...
  7. C

    Finding the Maximum and Minimum Values

    Homework Statement Find the maximum and minimum values of 3x+3y+2z on the sphere x^2+y^2+z^2=1 . Homework Equations Use of LaGrange Multipliers (maybe?) The Attempt at a Solution I have no idea if LaGrange multipliers is the way to go or not, but I took the partial derivative...
  8. S

    Minimum wavelength when electrons strike phospor

    Homework Statement Assume electrons are accelerated through a potential difference of 20000 V inside a TV picture tube. What is the minimum wavelength that could be produced when the electrons strike the phosphor? Homework Equations W = qV The Attempt at a Solution I use the...
  9. S

    The minimum radius of a plane's circular path

    Homework Statement An 82 kg pilot flying a stunt airplane pulls out of a dive at a constant speed of 540 km/h. a) What is the minimum radius of the plane's circular path if the pilot's acceleration at the lowest point is not to exceed 7.0g. Homework Equations Fg = mg Fnet = mv^2/r Fnet = ma...
  10. R

    I have a question about HA, VA and minimum points

    Homework Statement For the function h(x)=\frac{x^2*e^x}{x} , which of the following are true about the graph of y=h(x)? I. The graph has a vertical asymptote at x=0 II. The graph has a horizontal asymptote at y=0 III. The graph has a minimum point Homework Equations...
  11. R

    I have a question about HA, VA and minimum points

    Homework Statement For the function h(x)=\frac{x^2*e^x}{x} , which of the following are true about the graph of y=h(x)? I. The graph has a vertical asymptote at x=0 II. The graph has a horizontal asymptote at y=0 III. The graph has a minimum point Homework Equations...
  12. S

    Statics force problem - Force required to be a minimum

    1. Homework Statement : If the resultant force acting on the bracket is required to be a minimum, determine the magnitude of F1. I understand how to solve problems like this, I just don't understand what it means when it says that the force is required to be a minimum. Any help would be...
  13. M

    Can Adding a Resistor Prevent Low Voltage to a HID Ballast?

    hi all, im sorry if this is a very basic question, i am installing a aftermarker HID kit on a vehicle with daytime running lights. the hid kit requires a 9-16v input. vehicles headlights have a power of 12v the daytime running lights give less than 9 volt, i believe it is 6 volts to the...
  14. F

    What Is the Minimum Speed Required for a Car to Jump Over Eight Cars?

    A student driver wants to make his car jump over eight cars parked side by side below a horizontal ramp. The vertical height of the ramp is 1.50 m above the cars, and the horizontal distance he must clear is 20 m. If the ramp is tilted upward so that the “takeoff angle” is 10° above the...
  15. C

    Variably Solving for Minimum Tangential Speed

    Homework Statement A ride at a carnival rotates about a vertical axis. When spinning fast enough the bottom is dropped and the rider sticks to the side. Find the minimum tangential speed so that the rider does not fall. R=radius of circle, u= coefficient of static friction and g represents...
  16. J

    Minimum coefficience of friction PLEASE HELP

    Homework Statement A box with a mass of 20N is tied to another box with a mass of 15N hung over a pulley on an incline of 10 deg. please find the minimum coefficience (mu) for remaining stationary Homework Equations Not too sure, F(mu)=(mu)N N being normal force The Attempt at a...
  17. T

    Minimum Force for Moving a Sled on a Horizontal Surface

    Homework Statement A sled is pulled over a horizontal surface where the kinetic coefficient of friction is .20. What is the minimum force necessary to keep the sled moving if its mass is 2 slugs? Homework Equations fs = Ns(mg) The Attempt at a Solution fs = (.20) (2 slugs) (32)...
  18. M

    Minimum distance to avoid a collision

    Homework Statement While learning to drive, you are in a 1500 kg car moving at 19.0 m/s across a large, vacant, level parking lot. Suddenly you realize you are heading straight toward a brick sidewall of a large supermarket and are in danger of running into it. The pavement can exert a maximum...
  19. S

    Determining the Minimum Force to Push a Crate

    You try to push a crate of weight M with a force F on a horizontal floor. The coefficient of static friction is μs, and you exert the force F under an angle φ below the horizontal. Determine the minimum value of F that will move the crate. Okay so basically what i did was equate Mμs=Fcos φ and...
  20. V

    How Much Force to Pull a 1 Tonne Rock Up a 30 Degree Slope?

    1. A 1 tonne rock is being dragged up a 30 degree slope using the a pulley system. If there is a constant resistance to movement between the rock and the ground of 350N, calculate the minimum force necessary to drag the rock up the slope. 2. 3. All i got so far is 1t = 1000kg...
  21. I

    Boolean Algebra: Minimum Sum-Of-Products Expression

    Homework Statement Find the minimum Sum-Of-Product Expression for: f = ab'c' + abd + ab'cd' The Attempt at a Solution By introducing the missing variable in term 1 and term 2 I can get an expression that has all the variables: a, b, c, and d. I do so by: f = ab'c'd + ab'c'd' + abcd + abc'd...
  22. U

    Find the minimum distance between the curves

    Homework Statement Find the minimum distance between the curves (Parabola) y^2 = x-1 and x^2 = y-1 Homework Equations y^2 = x-1 x^2 = y-1 The Attempt at a Solution Tried to find the distance between their vertex, but the answer was wrong and no where near.
  23. K

    Quantum harmonic oscillator minimum energy

    http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc4.html#c1 I know the energy should be E = \frac{{{p^2}}}{{2m}} + \frac{1}{2}m{\omega ^2}{x^2} But I can't figure out why the minimum energy is related to \Delta p
  24. N

    What is the minimum potential for a bound state in a 3D potential well?

    finding minimum potential 1. Homework Statement A particle of mass m moves in 3-d in the potential well LaTeX Code: V(r)=-V_0 at LaTeX Code: r<r_0 where LaTeX Code: V0 and LaTeX Code: r_0 are positive constants. If there exists a state in which the particle is bound to the potential well...
  25. N

    Minimum Potential for Bound State in Spherically Symmetric Potential Well

    Homework Statement A particle of mass m moves in 3-d in the potential well V(r)=-V_0 at r<r_0 where V0 and r_0 are positive constants. If there exists a state in which the particle is bound to the potential well, the wave function for the bound state with the lowest energy is...
  26. J

    What is the Method for Finding the Local Minimum of a Function?

    Homework Statement Show that the function f(x) = \frac{x^8 + 9x^9 - 12x^{13}}{1 + x^3 - x^6} has a local minimum at x = 0. Homework Equations The Attempt at a Solution If f is to have a local minimum at x = 0 then we must have f'(0) = 0. Without typing up the tedious...
  27. E

    Minimum angle of resolution - units clarification

    Homework Statement A mouse has an pupil diameter of 2.5 mm. lying 200 meters from the mouse are two stones 30 cm apart. λ = 500 nm a) what angle do the stones subtend? b) what is the MAR (minimum angle of resolution) of the mouse's eye. Homework Equations question a) tanθ = O/A O= 0.3 m A= 200...
  28. G

    Living Off Minimum Wage and Pursuing a Physics Degree

    Currently I'm living in a relatively cheap apartment. I live off a minimum wage job making about $12 000 a year, which isn't much, but it is apparently a bit more than enough for how I live. I haven't gone through my undergraduate years in college (right now I'm gathering money). I want to do...
  29. maverick_starstrider

    Who is capable of achieving Landau's Theoretical Minimum in theoretical physics?

    If we define Landau's Theoretical Minimum (http://en.wikipedia.org/wiki/Lev_Landau#The_Landau_School) as roughly understanding ALL of the entire course of theoretical physics by Landau and Lifgarbagez, who thinks they would make the minimum? I know I sure as hell wouldn't. That requirement is...
  30. J

    Solving for Minimum Angle for Home Run

    Homework Statement the center field fence in a ball park is 10ft high and 400 feet from home plate. the ball is hit 3 ft above ground. it leaves the bat at an angle of theta degrees with the horizontal speed of 147.67ft/second. find the minimum angle at which the ball must leave the bat in...
  31. T

    Minimum Travel Time: Is It Possible?

    I was considering this the other day, and I'm pretty sure I know the answer, but I want verification that I am not missing anything. Suppose you are in a rocket ship and you want to travel, say, to a star the nearest galaxy. Is there a minimum amount of time that would require? Since the...
  32. P

    Center Tapped Full-Wave Rectifier minimum Io rating?

    http://img26.imageshack.us/img26/3844/fullwave.jpg Just as the title states I am having trouble calculating the minimum Io rating in a Center Tapped Full-Wave Rectifier. I thought it was I AVE x 1.2 but that has not seemed to give me the right answer. I would appreciate any help. (The scan...
  33. U

    Schools Minimum GRE scores for competitive grad school

    Hey everyone, I have heard over and over again that GRE scores are used by most engineering grad schools as a cut off; everyone above a certain score makes the first cut, and everyone below a certain score doesn't. I want to go to engineering grad school (specialize in biomedical). I took...
  34. C

    Minimum and maximum uncertainty values in quantum harmonic oscillator

    Homework Statement I have to find the minimum and maximum values of the uncertainty of \Deltax and specify the times after t=0 when these uncertainties apply. Homework Equations The wave function is Ψ(x, 0) = (1/√2) (ψ1(x)+ iψ3(x)) and for all t is Ψ(x, t) = (1/√2)...
  35. D

    How Many Minimal Broadcast Graphs Exist for a Given Number of Vertices?

    The "broadcast time" of a vertex v in a graph G is the number of time units it takes for a piece of information to go from v to every other vertex, provided that each vertex can communicate to only one other vertex during each time unit, and the information is transmitted in one time unit. The...
  36. S

    Normalized function and minimum energy

    please prove this: <Ψ|H\overline{^}|Ψ>\geqE0 function |Ψ> is normalized. prompt: (expand function |Ψ> in the eigenbasis of H operator, count average and use ortonormality of the H base) exercise 5.2.2 , p.163 , "principles of quantum mechanics" Shankar
  37. C

    Minimum compression of a spring.

    A toy car with mass 0.043 kg is propelled by a spring with spring constant 92 N/m onto a track. The track contains a vertical loop of radius 0.15 m. Ignore any losses due to friction and use g = 10 m/s2. What is the minimum compression of the spring necessary for the car to complete the loop...
  38. Loren Booda

    Average minimum tries for prime factorization

    On average, at least how many factors must one try dividing a number N by to decompose it into primes?
  39. S

    Minimum polynomial and canonical form

    Homework Statement Hi all. I have no clue on how to do this problem because I missed the class where he covered this so could someone please walk me through it. A = [2 2 -5; 2 7 2; -5 -15 -4] where ; means new column p(x) = (x-3)(x-1)^2 1) what are the choices of m(x) 2) find...
  40. R

    Finding an expression for the minimum drag coefficient

    Homework Statement I need to find an expression for the minimum drag coefficient, C_D, of an aircraft during straight and level flight. Homework Equations C_D=C_{D_0}+kC_L^2 Where: C_{D_0} is the profile drag coefficent C_L is the lift coefficient k is just a constant The Attempt at a...
  41. A

    F(x)=2x + 32/x find the absolute maximum and minimum if they exist

    find the absolute maximum and absolute minimum (if any) for the given function : f(x)= 2x + 32/x ; when x > 0 I tried to solve it but I'm not sure if its a maxima or minima, here are my try : f(x)= 2x + 32/x f'(x)= 2-32/x^2 2-32/x^2=0 2u^2=32 u^2=16 u=4 or - 4 -4 is not included...
  42. L

    Question about the minimum area

    Homework Statement hi guys, how are you all,, my friend had a quiz and he told me about this question : container has a square base and the volume of it V= 1000 , find the minimum area of the surface that the container can have ... Homework Equations A=x^2 , V=x^2 * h The Attempt...
  43. B

    Minimum Work Physics Problem | 65 kg Student Climbs 8.0 m Stairway in 12 s

    Homework Statement What is the minimum work done when a 65 kg student climbs an 8.0 m-high stairway in 12 s? The Attempt at a Solution v=d/t v=8/12 v=2/3 v = v2+v1 over 2 2/3 = v2+0 over 2 v2 = 2x[2/3] v2=4/3 w=deltaEk w=.5x65x[4/3]^2 - .5x65x0 w = 57 j ? answer is...
  44. Y

    Rotational energy, find minimum, for nitrogen molecule

    i made a mistake, and fixed it, but I'm still wrong. I totally thought I had this one. Little help here. Homework Statement What is the minimum (nonzero) rotational energy of the <sup>14</sup>N_2 molecule? Homework Equations E_rot = L * (L + 1) * E_0 * (m_e) / (4*M) M = (M_1 + M_2) /...
  45. Y

    Neutron, minimum potential energy, heisenberg uncertainty

    hi folks, last problem I can't get done here. I usually have a good idea of where to start, what to use. but I'm a bit flummoxed. Homework Statement A neutron, of mass m = 1.67 10-27 kg, is localized inside a carbon nucleus, of radius 7.0 fm (1 fm 10-15 m). Use the uncertainty relations...
  46. M

    Minimum Description Length for Features

    In minimum description length, you start with some programming language L, and some data D, and seek to find a program P in L such that evaluating P outputs D. You try to minimize the length of P, and you consider P to be a valid model of the data if the length of P is less than the length of...
  47. M

    Minimum angle required for resolution

    Homework Statement The radio telescope at Arecibo, Puerto Rico, has a reflecting spherical bowl of 295 m diameter. Radio signals can be received and emitted at various frequencies with appropriate antennae at the focal point of the reflecting bowl. At a frequency of 200 MHz, what is the...
  48. B

    Lagrange Multipliers to find the Maximum and Minimum values

    Homework Statement Use Lagrange Multipliers to find the Maximum and Minimum values of f(x,y) = x2-y. Subject to the restraint g(x,y) = x2+y2=25 Homework Equations gradient f(x,y)= gradient g(x,y) The Attempt at a Solution I have found the gradients of f and g to be f(x,y) =...
  49. S

    Minimum Length of Emergency Escape Ramp for Truck to Stop

    Homework Statement In Fig. 8-36, a runaway truck with failed brakes is moving downgrade at 130 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of θ = 15°. The truck's mass is 1.2 x 104 kg. What minimum length L must the ramp have if the...
  50. C

    Why have a minimum temperature

    Hi everybody...I have a sutupid questionf for you. Question is: Why have i a minimum temperature (-273 celsisus) and no maximum temperature in nature? Tanks...
Back
Top