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. 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...
  2. O

    Local Minimum of Potential Function of Spherical Pendulum

    Homework Statement http://img13.imageshack.us/img13/5793/84188411.jpg Homework Equations Find a condition on b such that x = 0 is a local minimum of the potential function. The Attempt at a Solution To find local minimum, potential function (V) of the system should be written. V...
  3. P

    How can I solve a constrained minimum problem?

    Hi, I need help with this problem; minimize x^3, subject to K= x-Ωπ so would the solution be K-Ωπ=x thanks!
  4. H

    Local minimum of z=(x^2+y^2)^(1/2)

    How do I find the local minimum of z=sqrt(x^2+y^2) I know its simple, but I'm stuck on it. I've tried using the second derivative but it just goes exponential. Then I tried using the second derivative test but did'nt succeed. And kindly could someone solve it step by step as it makes it much...
  5. M

    A thermodynamic inequality (from minimum work)

    EDIT: Turns out, the solution to my question is related to the determinant of a positive definite quadratic form. This is more or less straight from Landau's Statistical Physics Part 1 (3rd edition), Chapter 21. I don't understand how the inequality/condition (the last equation in this post)...
  6. C

    Critical number, max & minimum value

    Hey guys, I seem to have some troubles solving these problems. I was hoping if you guys can give me some insight. Thank you so much for your help! Homework Statement Find the absolute min and max value of each function Homework Equations f(x) = sin 2x - 2 sin x on (-pi,pi) The...
  7. C

    Can a Point Be Both a Local Minimum and Maximum?

    Hey forum I got to submit this in a few hours so if anyone could help me with this quick times, you would really be saving me :P Homework Statement Given the following graph of h(x) I only need help with part b) which asks for the local minimum or maximum points of the graph...
  8. T

    Find the minimum velocity for bucket in circular motion

    Hey, first of all I'm not looking for the answer I just want a nudge in the right direction :) Homework Statement "a bucket of water is rotated in a vertical circle of radius 1.00m. What is the buckets minimum speed at the top of the circle if no water is to spill out? Homework...
  9. S

    Find the maximum and minimum values of the function (Answers included).

    Homework Statement Find the maximum and minimum values of the function f(x,y) = 2x^2 - 28xy + 2y^2 - 1 on the disk x^2 + y^2 <= 1. (a) Find the maximum. (b) Find the minimum. Homework Equations Lagrange Multiplier method and partial differentiation. The Attempt at a Solution...
  10. K

    What is the minimum angular distance from the Sun for Venus to be visible?

    What is the minimum angular distance from the Sun for Venus to be visible TO THE NAKED EYE?
  11. T

    Minimum amount of friction in a turn

    Homework Statement What minimum coefficient of friction between the tires and the road will allow a 3700 kg truck to navigate an unbanked curve of radius 25 m at a speed of 45 km/h? Homework Equations The Attempt at a Solution The minimum coefficient is 7.62. To arrive at this...
  12. N

    Finding the minimum of an unknown function by the least amount of tries

    Homework Statement I am working on a program that queries an electronic instrument in order to find a value x for which the instrument will return a minimum value. I can provide any value for x that I want and the instrument will return the result f(x). The function has only one minimum. In...
  13. J

    A function without a maximum and a minimum

    Homework Statement Give an example of a non-continuous function on [0,1] that has no maximum and no minimum. Homework Equations Well, a continuous function on a non-empty compact set will have a maximum and a minimum, so I guess this is why we need a non-continuous function. The Attempt at...
  14. T

    Minimum number of elements to in one set to sum to all in another.

    Is there a name for the concept of trying to find the minimum number of elements from one set of integers that will sum to all elements in another set? Like, for example, with the Pythagorean Theorem, this would be to find the minimum number of elements from the set of all squared integers that...
  15. M

    Help finding minimum Tension that a rope can withstand without breaking

    Homework Statement A person of mass M stands in the middle of a tightrope which is fixed at the ends of two buildings separated by a horizontal distance L. The rope sags in the middle, stretching and lengthening the rope slightly. a)If the tightrope walker wants the rope to sag vertically...
  16. xpell

    Spaceport maximum and minimum inclination?

    (I'm not sure if this would be a 'school-type' question... it's definitively not for any kind of homework, so I'm posting it here, please relocate if appropiate) I've recently learned that spaceports have a maximum and minimum launch inclination, and that minimum inclination corresponds to...
  17. P

    Minimum Speed for the Water to not spill

    How is it that the water in a bucket, spun fast enough, does not spill? The formula at the top would be Total Force = Tension + M*g right? So would the tension be let as 0? If so, why? I can't understand how the water just simply does not fall out of the bucket :confused:
  18. K

    How Do You Determine the Extrema of f(x, y) = x + 2y on a Unit Disk?

    Find the maximum and minimum values of f(x,y) = x+2y on the disk x2+y^2 ≤1 I have this for now: f_1(x,y) = 1 f_2(x,y) = 2 x=cos(t) and y=sin(t) I have that g(t) = x(t) + 2*y(t) --> g(t) = cost(t) + 2*sin(t) g'(t) = 0 = 2*cost-sin(t) Then I can see that: 2cos(t)/cos(t)...
  19. E

    Minimum Minimum Power of a Heat Engine to freeze 50kg water in one hour

    Homework Statement Fifty kg of water at 0oC must be frozen into ice in a refrigerator. The room temperature is 20oC. The latent heat of fusion of water is 3.33x105 J kg-1. What is the minimum power required if the freezing is to take place in one hour? m = 50 kg Lf = 3.33x105 J kg-1...
  20. H

    Find the minimum separation between 2 pucks

    Homework Statement Two frictionless pucks are placed on a level surface with an initial distance of 20m. Puck 1 has a mass of 0.8 kg and a charge of + 3x10^-4 C while puck 2 has a mass of 0.4 kg and a charge of +3 x10^-4 C. The initial velocity of puck 1 is 12 m/s [E] and the initial...
  21. K

    Finding the maximum and minimum values

    I am having trouble with getting started with this one: Find the maximum and minimum values of f(x,y)=x+2y on the disk x^2+y^2 ≤ 1 I have started like this: fx(x,y) = 1 fy(x,y) = 2 and then I am lost...How do I solve it?
  22. N

    Finding the minimum speed of a proton traveling between two parallel plates.

    A proton, mass 1.67 x 10^-27 kg , is projected horizontally midway between two parallel plates that are separated by 0.8 cm , with an electrical field with magnitude 7.2 x 10^5 N/C between the plates. If the plates are 4.70cm long, find the minimum speed of the proton that just misses the lower...
  23. M

    Minimum magnetic field detected and measured

    hello! what is the minimum magnetic field that can be detected and measured? which organ does it? thanks!
  24. F

    Estimate the relationship between the maximum and minimum intensity

    Two speakers A and B are separated by 1 meter, the point P is 4 m away from speaker B. If P is a person for what frequency does he hear that the intensity have a minimum?. (The listener hear that the sound intensity reduces and increases).I don't know the distance from P to B. (They form a...
  25. F

    For what frequency does the intensity have a minimum?

    Two speakers A and B are separated by 1 meter, the point P is 4 m away from speaker B. If P is a person for what frequency does he hear that the intensity have a minimum?. (The listener hear that the sound intensity reduces and increases).I don't know the distance from P to B. (They form a...
  26. W

    News Right to vote = minimum of $1.00 federal tax.

    I wonder if they'll adopt my idea that only (federal income) taxpayers (minimum $1.00) should be allowed to vote?
  27. A

    Mathematica Finding Minimum Value with Mathematica

    ∂ω2 = (1-cos2(Δt)e-2γ(t))/(nTtsin2(Δt)e-2γ(t)) n,T are assumed as constants. How can I use Mathematica to find the values of Δ and t that will give the minimum values for ∂ω2 ?
  28. J

    Minimum kgf/N for a 4m x 2.5m Door - Outdoor Wind Resistance

    Hi What is the minimum kgf (or N) of a magnet to hold a 4m x 2.5m door? The door will be outdoor and wind can hit it. The function of the magnet is to keep it open. Best regards josh
  29. D

    Solving the IVP and minimum value

    Homework Statement Solve the initial value problem y' = 2cos (2x)/(3+2y), y(0) = 1 and determine where the solution attains its maximum value Homework Equations The Attempt at a Solution I got it to here y^{2} + 3y = sin(2x) + C but I don't know what to do from here... Help please
  30. P

    Finding the Minimum Angle for a Particle to Reach (x1,z1) from (0,0)

    Homework Statement A particle of mass m and initial velocity v0 is at (x,z)=(0,0) at t=0. The particle should hit the point (x1,z1). What is the angle for which the velocity is minimum? (Constant gravitational field -g in the z direction) Homework Equations v0x = v0*cos(theta) v0z =...
  31. Loren Booda

    How does maximum symmetry compare to its corresponding minimum symmetry?

    In a mathematical system, what similarities are there between the most and least absolute symmetries? Might Noether's theorem explain this?
  32. B

    Minimum bounding box problem

    Hi, I'm working at a small company currently trying to create a casting mould for double curved surfaces. I'm in charge of programming, and I'm creating a plugin for Rhino which is supposed to take a double curved panel and reorient it to the xy-plane from where it is read and sent to our...
  33. P

    Linear Motion - Minimum Retardation to Avoid Crash?

    First post! I would be grateful if anyone could give me any advice on this particular type of problem (i.e min retardation to avoid a crash). I'm not necessarily looking for the answer to this specific question, I would rather if someone could point me in the right direction as to how to go...
  34. D

    Rearranging a matrix to get the minimum diagonal

    Dear all, I have the following problem: I have a symmetric (non sparse) matrix, and I want to find the permutation of columns and rows that lead to have the smaller numbers in the diagonal. Anyone has a clue on how to solve efficiently this kind of problems? Thanks!
  35. K

    Unconstrained optimziation: Local minimum

    Homework Statement Theorem: Let f: M->R where M is a open subset of Rn Suppose f is C2(M) Let x E M such that "gradient of f at x" = 0 and the Hessian of f at x is positive definite Then x is a strict local minimum point of f. The above theorem is given in my textbook. If instead...
  36. A

    Finding the Minimum Non-Zero Element of a Set

    Hi there, As part of my paper I need to define the minimum non-zero element of some set. In particular I have, \begin{equation} \zeta(j):= \displaystyle \min_{\substack{ k\in1..\kappa\\ t\in 1..\kappa+1,~i \in \mathcal I^{t,j},\\ b_i^{t,j} \mod \theta_k \neq 0}} b_i^{t,j} \mod...
  37. L

    How to Determine the Minimum Number of Buses Needed Based on Arrival Times?

    How to calculate minimum number of buses that have to be used if I know arrival times in a bus stop? Regards
  38. O

    Find the minimum SOP function (Karnaugh map)

    first i hope is the correct forum to ask this kind of question. so i asked to find the minimum SOP function from the Karnaugh map (given in the picture). so i started to solve it as you can see in the picture. and this what i got:fsop=AB+BC+ACD'X' till here i think is ok. now this is...
  39. PainterGuy

    How to reduce this function to minimum form using K-map

    Hi :) Please have a look on the attachment to see my question. Please help me with it. Thanks Cheers PG
  40. M

    Location of minimum change in velocity for orbit escape

    Homework Statement A rocket is in elliptic orbit about the earth. To put it into escape velocity, its engine is fired briefly, changing the rocket’s velocity by deltaV . Where in the orbit, and in what direction, should the firing occur to attain escape with a minimum value of deltav...
  41. B

    Minimum safe distance to black hole

    I wonder what the minimum safe distance would be for a black hole with mass of a couple of billion solar masses. With that I mean at what distance would the gravitational pull be negligible, I guess. I am sorry if this is the wrong kind of question to ask in this forum.
  42. B

    Triple Integral of minimum value

    Homework Statement The problem is to take the triple integral over B of min{x,y,z}dV where B = {x,y,z}: o<x<1 , 0<y<1, and 0<z<1. (These are all less than or equal to, I didn't know the notation). Homework Equations The Attempt at a Solution What I did was break it up into...
  43. T

    Finding maximum or minimum of volume of solid revolved about a region

    Question: For c>0, the graphs of y=(c^2)(x^2) and y=c bound a plane region. Revolve this region about the horizontal line y= -(1/c) to form a solid. For what value of c is the volume of this solid a maximal or minimal (Use calculus 1 techniques). First, I found the volume of this...
  44. T

    TeX loves LATEXDoes F=x2y2-2x-2y have a minimum at the point x=y=1?

    Homework Statement Decide whether F=x2y2-2x-2y has a minimum at the point x=y=1 (after showing that the first derivatives are zero at that point). Homework Equations FxxFyy-Fxy2 The Attempt at a Solution So I found that: Fx=2xy2-2, which at point (1,1) = 0 OK Fy=2x2y-2, which...
  45. T

    Finding probability of a minimum

    let X1 and X2 be two randomly selected random variables from the same discrete distribution. Let Y=min(X1,X2). Find P(Y=1) according to the book. P(Y=1)=P[(X1=1)and(X2>=1)]+P[(X2=1)and(X1>=2)] I don't understand why is the asymmetry is even possible. The way I look at it, it's...
  46. K

    Determining Minimum Height for Marble to Complete Loop-the-Loop

    Homework Statement A marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off? Homework Equations What minimum height h must the...
  47. I

    How to Find Minimum Chi Squared Estimate for Flux (Fo)?

    hi i have some data (star counts) and i have a model and i want to perform min chi squared so if i call my data di, and my model mi with std dev = \sigmai = 1 then \chi^2 = \sum \frac{(di - mi)^2}{\sigma i^2} no my model is this mi = bi - Fo where bi is the background which has been...
  48. D

    Minimum distance between a point and a bounded line in 3D

    I have a point in 3D specified by its coordinates (x0, y0, z0) I have a line in 3D specified and bounded by its end points (x1, y1, z1) and (x2, y2, z2) How do I calculate the minimum distance between the point and the line, keeping in mind that it may not be the perpendicular distance...
  49. P

    Friction, Statics, Finding maximum angle and minimum coefficient of friction

    Homework Statement If the coefficient of static friction at B is μs = 0.3, determine the largest angle θ, and the minimum coefficient of static friction at A, so that the roller remains self- locking, regardless of the magnitude of the force P applied to the belt. Neglect the weight of...
  50. V

    What is minimum value of |a+bw+cw^2|? whrere w is cube root of unity?

    a,b,c are integers not all equal and w is the cube root of unity then minimum value of |a+bw+cw2|(w is not equals one). My answer |a+bw+cw2|<=|a|+|bw|+|cw2| |a|+|bw|+|cw2|=a+b+c. so at lest one value of |a+bw+cw2| will smaller than the minimum value of a+b+c. for integers this minimum...
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