What is Maximum: 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. javii

    Calculate the maximum acceleration of a milk carton

    Homework Statement Homework Equations ∑Mb = m*a*d The Attempt at a Solution Using the formula below i get: m*g*cos(0)*(0.07/2)-m*g*sin(0)*(195/2)=m*a*h And I get 3.52 m/s^2 Is it correct?
  2. H

    Increase the maximum voltage rating of semiconducter

    Hello, I was wondering if there is any way of increasing a transistor or thyristor maximum voltage ratting in DC? Thanks. Edit: Just to be more precise, I am referring to the off state. I know you can the on state via a resistor.
  3. V

    Question about Maximum Entropy

    The second law of thermodynamics predicts the end of the life of the universe being one where thermal equilibrium exists throughout the universe (maximum entropy) - essentially all energy has been dissipated. My question is if according to the first law of thermodynamics which describes the...
  4. C_Pu

    Proving Carnot efficiency is maximum and conditions

    The standard proof to show carnot efficiency cannot be exceeded is to couple a supposedly more efficient engine to a carnot refrigerator, and show that it would violate second law. However, isn't it true that we can make the same argument with any arbitrary efficiency? Some discussions on...
  5. SlowThinker

    B Maximum efficiency of a dehumidifier

    There's a youtube channel where someone nicknamed Thunderf00t is making fun of a water source that is supposed to be a wind-powered dehumidifier. He makes some arguments that don't look entirely valid. He argues that the energy needed is the evaporation heat of water, or some 2000 kJ/kg. In...
  6. F

    Maximum coefficient of friction

    This issue was the subject of this old post, now closed. The question is: can a coefficient of friction (static) be larger than one? I see confusing replies. Someone talks about glue, but I'm not convinced about that. It's a bit like wondering about the coefficient of friction of a wooden plank...
  7. T

    Gradient and finding the direction of maximum rate of change

    Homework Statement Hi guys, it a very simple question, but it causing me a great deal of confusion. The questions are as follows: So I worked out the ans for one which I have displayed below. But what I don't understand is what they want from the second question. Because the way I see it...
  8. I

    Maximum area of triangle inside a square

    Homework Statement ##ABCD## is a square piece of paper with sides of length 1 m. A quarter-circle is drawn from ##B## to ##D## with center ##A##. The piece of paper is folded along ##EF##, with ##E## on ##AB## and ##F## on ##AD##, so that ##A## falls on the quarter-circle. Determine the maximum...
  9. M

    MHB Exploring the Global Maximum of a Differentiable Function

    Hey! :o I am looking at the following: The differentiable and so also continuous function $f:[a,b]\rightarrow \mathbb{R}$ gets its global maximum at a point $x^{\star}$. Show that the following holds $$f'(x^{\star})=\left\{\begin{matrix} =0\\ \leq 0\\ \geq 0 \end{matrix}\right. , \ \text{...
  10. B

    Maximum vapor velocity from a heat exchanger into a turbine

    Hi Everyone, I am looking at designing a small impulse steam turbine that runs off of saturated refrigerant vapor delivered from a shell and tube heat exchanger. With the design of the turbine, I am looking to maximize the velocity that the steam can exit from a diverging nozzle in order to be...
  11. A

    What is the Strategy for Evaluating Minimum and Maximum Values in Calculus?

    Homework Statement The problem is in the attached file. The part I need a little help with is part b. Homework Equations and attempt at a solution[/B] For part a, I got h(8) = 2, h'(6) = -2, and h''(4) = -2. For part c, I found that the integral from 0 to 5 is 7, so I multiplied 7 by 7 to...
  12. T

    Maximum temperature reached by gas in expansion

    Homework Statement 1 mole of ideal gas with internal energy U= 3/2 RT , expands from initial volume Vi = 1/10 Vo following the equation p=(− po / Vo ) V +po . Find (a) the highest temperature reached by the gas during the expansion and (b) the maximum amount of heat taken in by the gas...
  13. Ashley Leong

    How does drag force change the maximum height of projectile?

    How does air resistance change the maximum height of a projectile ?
  14. J

    I Maximum tangential velocity from maximum linear velocities

    I have a particle that moves along a circular arc centered at origin in 2D plane. I have the following angular displacement function for time T0 through T3 and the following acceleration and velocity constraints in Cartesian coordinates. At t = T0, theta = 0, velocity = 0. At t = T3, velocity =...
  15. brenna_s

    How to find the equation for the maximum velocity possible

    Homework Statement When an object is moving in a vertical circle attached to a string, it can withhold a maximum tension at the bottom of it's path. Derive an expression for the maximum velocity the object can sustain without the string breaking. No data is given, and everything should be...
  16. EthanVandals

    What is the Maximum Height of this projectile?

    Homework Statement A projectile is launched at 750 meters per second at a 30 degree angle to the horizon. How long is it in the air? How far does it go? What is the maximum height that it reaches? Homework Equations Sin(30)=1/2 Cos(30)=sqrt(3)/2 The Attempt at a Solution This is what I have...
  17. lfdahl

    MHB What is the maximum and minimum sum for $|a-b|+|b-c|+|c-a|$ with given relation?

    Find the maximum and minimum of the sum $|a-b|+|b-c|+|c-a|$, if the integer numbers $a,b$ and $c$ satisfy the following relation: \[ (a-b)^3+(b-c)^3+(c-a)^3 = 60 \]
  18. T

    Maximum likelihood of a statistical model

    Homework Statement I look at the distribution ##(Y_1,Y_2,...,Y_n)## where ##Y_i=μ+(1+φ x_i)+ε_i## where ##-1<φ<1## and ##-1<x_i<1## . x's are known numbers. ε's are independent and normally distributed with mean 0 and variance 1. I need to find the the maximum likelihood estimator for μ and...
  19. J

    Maximum velocity for the motor movement

    Hello all, First of all let me say this is my first post here and I don't know if I'm placing it into the right forum/place. If I'm doing something wrong or similar, please let me know and I'll try to solve it asap. This is not homework, but it is for sure introductory level so I've thought...
  20. Arup Biswas

    Why subsidary maximum has lower intensity physically in single-slit diffraction?

    In single slit diffraction the subsidary maximum has lower intensity than of central. Yes mathematically from the intensity equation we can see that. But how physically we can explain that? When the central and the 1st maxima has same activity to produce constructive interference( as in same...
  21. axutio

    Building a wall to reduce maximum collision force

    Homework Statement I was recently assigned a project of, tl;dr, building a wall to reduce the maximum force during a collision. Let me start by describing the setup as best as I can. First, here's an image: These aren't the exact track and carts we're using, but they provide a great...
  22. F

    Maximum shear acting on a point

    Homework Statement Why we need to consider only 3 cases when we want to find the max positive shear ? Homework EquationsThe Attempt at a Solution IMO , We know that the max shear will only occur when the 67.5kN act on B , am i right ? There is no need to consider 3 different cases ...Or my...
  23. Davephaelon

    I Maximum practical size of a BEC

    It's technically very difficult to create BEC's of atoms, using lasers to cool the atoms to near absolute zero, in a vacuum chamber, and it was only first accomplished in 1995, despite being predicted many decades before that. The atom, or molecule, BEC's so far created are, from what I've...
  24. V

    Finding Maximum Velocity in Train Motion

    Homework Statement A train travels a distance of 1,2 km between two stations with an average velocity of 43.2 km/h. During it's motion, at the time t1=40s it moved accelerated, then at time t2 it moved uniformly, then at t3=40s it moved uniformly slowed. Find the maximum velocity of the train...
  25. N

    Max Load Force on Uniform Pine Beam of 3.6m & 25kg | Safety Factor 5.0

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  26. R

    Maximum potential energy after collision

    Homework Statement : A ball a, moving with kinetic energy E, makes a head on elastic collision with a stationary ball with mass n times that of A. The maximum potential energy stored in the system during the collision is a)nE/(n+1) b)(n+1)E/n c)(n-1)E/n d)E/n[/B]Homework Equations :Principle of...
  27. Aleph_null

    Find the minimum and maximum of a ratio for equilibrium

    Homework Statement Consider the rod as shown in the figure. The coefficient of static friction at A and B is \mu_s. I'm trying to find how big and how small the ratio l/d can be for the rod to still be in equilibrium. I have calculated how big all forces are acting upon the rod in the case...
  28. F

    Angle of principal stress vs maximum shear stress

    Homework Statement I'm having problem with the angle of $$theta_s1$$ . My ans is +35 (as in my working) , but the ans provided is $$theta_s1$$ = -55[/B] Homework EquationsThe Attempt at a Solution As in the picture posted
  29. F

    Maximum shear stress in Mohr's circle

    Homework Statement I am not sure how to get the maximum shear force in mohr's circle [/B] Homework EquationsThe Attempt at a Solution To get the ##\theta_s max ## , we have to 'turn' the B to ##\tau_{max}## , right ? So , it should be like this ( in the figure , orange arrow) ? Am i right ...
  30. A

    Maximum force so object on top wouldn't start sliding back

    Homework Statement Box B is on top of box A. Box A has a mass of 1 kg, B has 0.3 kg. Coefficient of friction between ground and box A is 0.5, between box A and B : 0.75. With what maximum force can I pull box A without box B sliding back ? m1 = 1 kg m2 = 0.3 kg u1 = 0.5 u2 = 0.75 Homework...
  31. O

    Maximum Power Transfer Ideal Transformer

    Homework Statement Given the following circuit find the value of ZL for maximum average power transfer and find the maximum power. Homework Equations n = N2/N1 V2/V1 = N2/N1 I2/I1= N1/N2 The Attempt at a Solution move ZL from the secondary coil to the primary coil using Zs* = ZL/n^2 ZL =...
  32. harini07

    General organic chemistry -- finding maximum electron density

    Homework Statement In pyrrole the electron density is maximum on which carbon atom? so if the numbering starts from nitrogen, the carbon on the right side of nitrogen let it be numbered as 2 and the next one as 3 and so on... which of the following options will have the carbons of maximum...
  33. J000e

    Understanding Maximum Moment for Moving Loads: Strength of Materials Reviewer

    Hey guys, I've been reading my strength of materials textbook and its pretty much like a reviewer that contain several problems and short descriptions of their concepts. There's this formula that computes the maximum moment for two moving loads and its: [PL-(Psmall)(d)]^2/4PL where P= Psmall...
  34. A

    How to find maximum force on a velocity vs time graph

    The velocity versus time graph is the following: http://imgur.com/kyebx8H As the title asks, how would you find the maximum force on a velocity vs time graph given nothing but the graph and the mass of the object in question. My reasoning was that since f = ma and m is never changing, that...
  35. E

    How to maximum apparent power through a linear transformer?

    Homework Statement given a linear transformer rated for 50kVA, 11000V/120V How do I find the maximum apparent power? The prompt is to maximum apparent power while keeping the Load RMS voltage between 114V and 126V. Vsource has a peak voltage of 11000*sqrt(2). The circuit looks something like...
  36. sliperyfrog

    The maximum magnitude of the electric field of a sphere

    Homework Statement A non-conducting sphere of radius a carries a non-uniform charge density. The electrostatic field inside the sphere is a distance b from is center and is given by E = (b/a)4E0 (E0 being the maximum magnitude of the field.) a. Find an expression for E0 in terms of the...
  37. F

    Maximum slope of deflection of beam

    Homework Statement why the author said that by inspection , the maximum slope occur at D ? How do we know that ? He didnt show the working and explanation . Homework EquationsThe Attempt at a Solution If I consider the maximum slope to occur at a point after 2m from A , then i will take...
  38. surya teja saithana

    Torsional spring and maximum velocity of wheel

    Moderator's Note: HOMEWORK POSTED IN WRONG THREAD, SO NO TEMPLATE Thread title changed to make it descriptive of the problem. can i solve this question using energy conservation method as shown.
  39. doktorwho

    Calculate the maximum electrical force on a ball

    Homework Statement A metal ball of radius ##a## is at a distance ##h>>a## from a very long conducting non-charged horizontal metal surface. Calculate the maximum electrical force on a ball under the condition that ##E_{cr}## the critical electric field of air is not breached. Homework Equations...
  40. G

    Finding maximum height of a string before it goes slack

    Homework Statement A mass m is suspended by a light elastic string. When the mass remains at rest it is at a point 0, which is a distance a + b below the point from which the string is suspended from the ceiling, where a is the natural length of the string. The mass is pulled down a distance h...
  41. F

    Maximum deflection / slope of beam

    Homework Statement As in the diagram Homework EquationsThe Attempt at a Solution For part a ) , my ans is EI(d2y/dx2) = - Px For part b) , my ans is EI(dy/dx) = -P(x^2)/2 +c1 EIy = -P(x^3)/6 +c1x +c2 at x= 0 , y = 0 , so c2 = 0 , at x = 0 , dy/dx = 0 , so c1 = 0 , so , EIy = -P(x^3)/6 ...
  42. anemone

    MHB What is the maximum value of $a^2b$?

    Let $a$ and $b$ be positive real numbers such that $a+b+\sqrt{2a^2+2ab+3b^2}=4$. Determine the maximum value of $a^2b$.
  43. Vanessa Avila

    The ball's maximum speed relative to the vehicle?

    Homework Statement Inside a NASA test vehicle, a 3.50-kg ball is pulled along by a horizontal ideal spring fixed to a friction-free table. The force constant of the spring is 226 N/m . The vehicle has a steady acceleration of 5.00 m/s2, and the ball is not oscillating. Suddenly, when the...
  44. E

    What is the maximum energy of the Λ particle after the Σ0 baryon decay?

    Homework Statement A Σ0 baryon, traveling with an energy of 2 GeV, decays electromagnetically into a Λ and a photon. What condition results in the Λ carrying the maximum possible energy after the decay? Sketch how the decay appears in this case, and calculate this energy. Explain your...
  45. TheDemx27

    Find the Maximum of Superposition of Waves

    Homework Statement Two waves are produced simultaneously on a string of length L = 1 m. One wave has a wavelength λ of 0.5 m. The other wave has a wavelength λ of 0.2 m. The amplitudes of the waves are the same. At t=0, at what locations x0 is the displacement y(x0) equal to zero? At what...
  46. bluejay27

    I What is the maximum size of a Quantum Dot?

    What is the maximum size of a Quantum Dot? What are the limits of the size of the quantum dots? At what size do we stop calling a Quantum Dot a Quantum Dot?
  47. evinda

    MHB Maximum principle for subharmonic functions

    Hello! (Wave) I have a question about the proof of the maximum principle for subharmonic functions. The maximum principle is the following: The subharmonic in $\Omega$ function $v$ does not achieve its maximum at the inner points of $\Omega$ if it is not constant. Proof: We suppose that at...
  48. N

    How to find the maximum induced current for a diamond-shaped loop?

    Homework Statement Find the total maximum induced current for the diamond-shaped metal loop that is moving at a speed of 10 m/s towards a uniform magnetic field of 0.8T. All four lengths equal 10 cm or 0.01 m. Homework Equations emf = -dΦB/dt ΦB=∫B*dA A = (1/2)bh The Attempt at a Solution I...
  49. J

    Dynamics how to calculate maximum height on incline

    Homework Statement A 5.0kg block initally traveling at 11m/s moves up a 30degrees incline. A frictional force of 9.4N acts on the block as it moves up the incline. What maximum vertical height, h, will the block reach? m = 5.0kg, vi = 11m/s, vf = 0m/s, Fr = 9.4N, Homework Equations...
  50. pluviosilla

    I Why is the Maximum Likelihood Function a product?

    Why is the Maximum Likelihood function a product? Explanations of how the Maximum Likelihood function is constructed usually just mention that events are independent and so the probability of several such events is just the product of the separate probabilities. I get the logic w.r.t...
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