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. SamRoss

    I Missing exponent in "Theoretical Minimum"?

    In "The Theoretical Minimum" (the one on classical mechanics), on page 218, the authors write a Lagrangian $$L=\frac m 2 (\dot r^2 +r^2\dot \theta ^2)+\frac {GMm} r$$ They then apply the Euler-Lagrange equation ##\frac d {dt}\frac {dL} {d\dot r}=\frac {dL} {dr}## (I know there should be...
  2. W

    Find the force of Friction and minimum coefficient of friction

    Fg = mg = 50 * 10 = 500 N Fn = mg-ma = 500 - (50.0)(1.0) = 500-50 = 450 I don't necessarily know if this is right and I can't seem to find the Ff or coefficient of friction either. Please Help!
  3. themountain

    The magnitude and direction of the minimum magnetic field

    F=ILB F=(48)(.76)B F/36.48=B I am stuck at how to find F, is there a different formula I am missing?
  4. EEristavi

    2 objects connected by a spring - Minimum Force required to move the objects

    On object 2: There are only 2 horizontal forces - Friction and Tension (of the spring). T = km2g On Object 1: There are 3 horizontal forces and the minimum value for F is when: F - km1g - km2g = 0 F = kg(m1 + m2) However, Solution is: F = kg(m1 + 0.5 m2) Any opinion?
  5. C

    Electrical Minimum conduction voltage between aluminium plates exposed to air?

    Hi, just thinking about a possible project and it may involve bolting aluminium plates together and putting a very small voltage across them. If I take two plates of aluminium, leave them to oxidise in air (we all know Al forms a surface layer) then is there a minimum voltage that will flow...
  6. K

    Minimum energy positron electron collision producing Z-boson

    Homework Statement Homework Equations m2 = E2 - p2 ([/B]The Attempt at a Solution I got stuck by not knowing how to handle the frames and I thought you can view the Z boson (CoM) frame, but then you simply get that mz = 2me
  7. N

    Finding the Parameters for the Curve y=asin(x-b)+c

    <Moderator's note: Member has been informed to separate different question into different threads in the future.> 1. Homework Statement Please see picture attached... The diagram shows the curve with equation y = f (x) The coordinates of the minimum point of the curve are (–2, –1) (a) Write...
  8. Q

    Boat with Friction: CoM / Minimum Time Problem

    Homework Statement A person of mass ##m## stands at the left end of a boat of mass ##M## and length ##L##. Both the person and the boat are initially at rest. The coefficient of kinetic friction between the boat and the water is ##\mu##. If the person starts moving to the right, what is the...
  9. R

    Space elevator minimum initial speed

    Homework Statement In the far future, humans have built a space elevator as a cheap means of access to space. However before that could be done, a few basic principles had to be worked out. . . a) What is the minimum initial speed (in an Earth-centered inertial reference frame) needed for an...
  10. PhysicsKT

    What is the optimal angle for an ant to climb a wire and gutter?

    Here's the problem: https://i.stack.imgur.com/rUVvu.png What I did: [2]: https://i.stack.imgur.com/AX2Ye.png [3]: https://i.stack.imgur.com/K1Zbi.png To those who could not understand what I read: So basically I used some geometry to to get $l_1$ and $l_2$ in terms of $r$ and the assumed...
  11. hnnhcmmngs

    Minimum heat removed from gas to restore its state

    Homework Statement After a free expansion to quadruple its volume, a mole of ideal diatomic gas is compressed back to its original volume isobarically and then cooled down to its original temperature. What is the minimum heat removed from the gas in the final step to restoring its state...
  12. V

    MHB The minimum and maximum of a sequence

    I have the following sequence: $x_{n}=(-1)^{n-1}\cdot \left(2+\frac{3}{n}\right),\forall n\in \mathbb{N^{*}}$ I need to choose from: A. $x_{n}$ is a monotonic sequence B. $x_{n}$ limit is $2$ C. $x_{n}$ minimum is $-\frac{7}{2}$ and the maximum is $5$ D. $x_{n}$ minimum is $-2$ and the maximum...
  13. J

    Minimum and maximum values so the system remains at rest

    Homework Statement [/B] Two blocks A and B of masses m and M are connected to the two ends of a string passing over a pulley. B lies on plane inclined at angle theta with the horizontal and A is hanging freely as shown. The coefficient of static friction between B and the plane is us. Find the...
  14. Z

    "The theoritical minimum" modern equivalent for solid state?

    Hi, for those who don't know, Landau (Lev Davidovitch Landau) had a famous exam called "The theoretical minimum". That exam had to be passed by any future grad-student of his. That test was extremely extensive and difficult, and the student was supposed to be knowledgeable about many fields of...
  15. C

    Finding the minimum number of boxes to pack products

    Homework Statement This was a coding challenge, and I've already completed it. But I feel there must be a better solution to my approach at the moment. Especially maybe there's a mathematical approach. You have 3 sizes of boxes, small, medium, large: small: holds 3 items medium: holds 5 items...
  16. J

    Uncertainties and the angle of minimum deviation

    Homework Statement For a physics experiment I need to find the uncertainties and I am using the angle of minimum derivation formula: The value of A=60° and one of the values of D is 29.7° which has a uncertainty of ±2 (I know it's a very high value) Homework Equations How do I calculate the...
  17. W

    Maunder Minimum & Climate Change

    We all know that our CO2 emissions will warm the planet. However I am wondering to what extent do climate models include the view that we might be heading to a new Maunder Minimum? https://www.nextbigfuture.com/2018/11/winter-is-coming-super-grand-solar-minimum.html Will this buy us a bit more...
  18. J

    Minimum deceleration to prevent a collision

    Homework Statement At a given time ##t=0##, a car 1 moving with constant velocity ##v_{1}## breaks with constant deceleration ##d##. Another car 2 at a distance ##L## behind car 1 and traveling with constant acceleration ##a_{2}## and velocity ##v_{2}## at ##t=0## brakes immediately as soon as...
  19. Krushnaraj Pandya

    The minimum of a function in a given domain

    Homework Statement The operating cost of a truck is 12+(x/6) per km, when the truck travels x km/hr. If the driver earns 6 rupees (*or whatever currency your country has) per hour, what is the most economic speed to operate the truck on a 400 km road? Also, due to weather, the truck can travel...
  20. J

    Optimizing Periodic Motion in an Elliptical Orbit

    Homework Statement A particle moves periodically around an ellipse of equation ##\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1##. You can assume ##a>b##. The ##x## and ##y## components of the particle's velocity can never exceed ##v## at any point. What is the minimum possible period of the...
  21. Wi_N

    I'm looking for a local minimum point that doesn't show up when....

    Homework Statement I set the derivative to 0. i get 1 real root a max point and 2 imaginary. How can i find that local min? what techniques are available?
  22. J

    Maximum and minimum speeds in a moving cube

    Homework Statement A rigid cube in the figure moves in space. At a certain time ##t## its front face ##ABCD## is vertical and the velocity of vertex ##A## is vertical down ##v## while the velocity of its vertex ##D## makes an angle with the vertical and has magnitude ##v_{2}## while lying on...
  23. H

    Equation for sum of torques on a ladder and minimum angle

    Homework Statement [/B] Homework Equations Drawing a diagram for the forces is the easy part. I am not sure I am doing the equation of the sum of the torques well. The Attempt at a Solution This is my attempt for the forces[/B] And this for the torques:
  24. N

    How to find the minimum angular resolution?

    Homework Statement λ = 240 nm D = 2.40 m We are supposed to find the angle resolution (minimum angular distance between two objects so we still see them as two separate objects) to the telescope for ultraviolet light with wavelength 240 nm Homework Equations The equation that I used is θ =...
  25. Q

    The minimum inclination of a surface

    I am an IT student and working on a project, an automated system. It's not for a physics class. I can't say exactly what the system can do. But it uses Arduino to dispense servings of grains on a given schedule. I am more of a programmer than a physicist, I am looking for help on this. 1...
  26. S

    Minimum Wire Length Calculation for Square Pattern in 10cm Square

    Homework Statement A wire pattern is inserted into a ##10##cm square by making a horizontal line in the middle of the square (not all the way across and with length ##x##) and connecting the ends of this line to the closest two corners. What is the minimum value of ##x##? Homework EquationsThe...
  27. M

    Minimum force before a system of two blocks will move

    Homework Statement [/B] ##m=3kg## ##M=2kg## Coefficient of static friction between m and M ##\mu_1 = 0.6## Coefficient of static friction between M and the ground ##\mu_2 = 0.8##. The rope is weightless, does not stretch, and the wheel is frictionless. What is the maximum force ##F## that...
  28. T

    Finding the minimum distance between two cars

    Homework Statement We have two cars moving like the picture. we want to find their minimum distance using relative motion. I) Consider a coordinate system on M, which has two axis. one axis is in direction of MP and the other is perpendicular to that (Something like r_hat and θ_hat). Find the...
  29. zehkari

    What is the minimum force at this angle that will move the box?

    Homework Statement [/B] 2. Homework Equations Fs = Nμ W = mg Fy = Fsin(θ) Fx = Fcos(θ) The Attempt at a Solution [/B] Hello all at PhysicsForums, I have a question on angled force and static friction. From my attempt below, I think I have found the maximum force required and would need...
  30. J

    Finding minimum force to pull the napkin out from under the tea cup

    Homework Statement There is a table, and a napkin on it. The napkin has a mass mn=71.6 g. On the napkin, there is a tea cup with mass mc=104.6 g. What is the minimum force required for someone to pull the napkin out from under the tea cup? Assume that between the table and the napkin the...
  31. D

    Minimum energy of an electron with the Larmor formula

    Homework Statement Is there a minimum value for the total energy of the electron (in this analysis)? The previous parts: Use Larmor formula to find ##\frac{|\Delta E|}{K}##, where ##|\Delta E|## is the energy lost per revolution. the result is ##\frac{8\pi v^3}{3c^3}##. ##\frac{v(r)}{c}## was...
  32. A

    Minimum Acceleration of an ambulance

    Homework Statement An ambulance driver is rushing a patient to the hospital. While traveling at 70 km/h, she notices the traffic light at the upcoming intersections has turned amber. To reach the intersection before the light turns red, she must travel 58 m in 2.5 s. 1. What minimum...
  33. P

    Energy: What will be the minimum ratio of m/M here

    Homework Statement The objects are set free from the scenario shown in the attached image. Their masses have been given and they are under the effect of gravity. The length of the string has been shown in the figure. If the two blocks cross each other, then we need to determine the minimum...
  34. baldbrain

    How do I find the minimum of 5a + b?

    Homework Statement If ax2 - bx + 5 = 0 does not have two distinct real roots, find the minimum value of 5a + b. 2. Homework Equations The Quadratic Formula The Attempt at a Solution Here, D = b2 - 4a(5) = b2 - 20a D ≤ 0 ⇒ b2 ≤ 20a ⇒ b ≤ ±2√(5a) Also, an obvious observation is that b ≤ 0...
  35. D

    Calculating Minimum Speed for a Successful River Jump

    Homework Statement A stunt motorcyclist has to jump across a river 7.0 m wide from a ramp on one side with incline of 10 degrees. (a) What minimum speed the motorcycle must have to successfully land on the opposite side of the river? (b) How long will the motorcyclist be in the air? (Assume...
  36. I

    Find the minimum value of area under y = 4x - x^3

    Homework Statement Find the minimum value of the area of the region under the curve ## y=4x - x^3 ## from ##x=a## to ##x=a+1##, for all ##a>0##. This problem is from Stewart's Calculus Homework Equations Finding the area under the curve... The Attempt at a Solution I can set up the equation...
  37. S

    Minimum breakdown voltage in Neon, Electrode spacing in mm

    Hello all. I am conducting a simple research project, and am having a little trouble with the math for paschen's law. my question is. At 74762 Microns of pressure, using pure Neon gas, what is the electrode spacing in mm for the minimum breakdown voltage of that gas? Thank you.
  38. M

    MHB F has an uniquely defined global minimum

    Hey! :o Let $a_1, a_2, \ldots , a_k\in \mathbb{R}^n$ and $f:\mathbb{R}^n\rightarrow \mathbb{R}$ defined by $\displaystyle{f(x)=\sum_{j=1}^k\|x-a_j\|^2}$ with the euclidean norm $\|\cdot \|$. Show that f has an uniquely defined global minimum and calculate it. I have done the following...
  39. Pushoam

    Determining maximum and minimum points of a projected circle

    Homework Statement Homework EquationsThe Attempt at a Solution This problem belongs to the topic "calculus of variation ". The fundamental problem of “calculus of variation” is to find a function y(x) such that the integral ## I = \int_{x_i }^{ x_f} \phi (y’, y, x) ~d x ## is extremum...
  40. JuanC97

    I Minimum requisite to generalize Proca action

    Hello guys, In 90% of the papers I've read about diferent ways to achieve generalizations of the Proca action I've found there's a common condition that has to be satisfied, i.e: The number of degrees of freedom allowed to be propagated by the theory has to be three at most (two if the fields...
  41. K

    Finding the minimum pass point

    Homework Statement A factory is hiring ##m## employees. A number ##n > m## of candidates applied to the job. They need to answer an exam consisting of questions all of equal weight. A candidate is selected to the next step (the interview) if he/she achieves a minimum of ##c## points in the...
  42. chrisritson

    Help Determining the Minimum Thickness of a Vacuum Chamber Lid

    Hello. I am attempting to build a large vacuum chamber for woodworking (used to infuse wood with resin/stabilizer). I would like to use a cast iron bathtub, similar to the one pictured as the vessel. I would ideally like to use a clear acrylic lid (with a rubber gasket) like the one on my...
  43. aphirst

    A Derivative of argmin/argmax w.r.t. auxiliary parameter?

    As part of my work, I'm making use of the familiar properties of function minima/maxima in a way which I can't seem to find in the literature. I was hoping that by describing it here, someone else might recognise it and be able to point me to a citation. I think it's highly unlikely that I'm the...
  44. Borek

    Minimum length of the Pitot tube?

    I have a thin tube (4 mm diameter) sticking out of a small box (a bit larger than a matchbox). I want to use this tube to measure the dynamic pressure. How long must the tube be for the results to be reasonably accurate? Intuition tells me the working end of the tube should be kept in the...
  45. H

    Find the minimum distance between 2 particles

    Homework Statement A point particle of mass m and charge q(>0) approaches to a point particle Q(>0) at a fixed position. When the distance between the two particles is L, the speed of the moving particle is v. The permittivity of the vacuum is denoted as Epsilon0. Find the minimum distance...
  46. Highwire

    [The Theoretical Minimum] Can closed systems exist?

    Homework Statement The first exercise in Susskind and Hrabovsky's The Theoretical Minimum is one that, in the words of Susskind, "is designed to make you think, more than it is designed to test you." The exercise asks: Homework Equations In the prior paragraph, the authors define the notion...
  47. S

    Boolean Algebra, Minimum Sum of Products Problem

    Hello to everyone who's reading this. The problem I need help with is the following.: Homework Statement "Simplify to obtain minimum SOP. F(A, B, C, D) = A’B’CD’+AC’D’+ABC’+AB’C+AB’C+BC’D" The problem stated above has two provided solutions, the "main" one and the "alternate" one. I'm...
  48. Irl495

    Minimum gas pressure to measure its volume with an eudiometer

    Hello, As you can see in the attached hand drawing+calculation, my question concerns the typical method of evolved gas volume measurement by water displacement in an inverted graduated cylinder or "eudiometer". Once a bubble (cavity to be precise) of gas leaves the end of the tube through...
  49. M

    MHB Determining the Maximum and Minimum of a Discontinuous Function $f(x,y)$

    Hey! :o We have the function $f: (\mathbb{R}^2,\|\cdot\|_2)\rightarrow (\mathbb{R},|\cdot |)$ with \begin{equation*}f(x,y)=\begin{cases}y-x & y\geq x^2 \\ 0 & y<x^2\end{cases}\end{equation*} I have shown that $f(x,y)$ is discontinuous at the points $(x,x^2)$ with $x\neq 0,1$ and continuous at...
  50. G

    Quantum Dr Susskind: Theoretical Minimum Quantum Field Theory?

    Does anyone know if or when Dr Susskind is coming out with a “ Theoretical Minimum Quantum Field Theory “ ?
Back
Top