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. H

    Maximum height reached by object released from a vertical spring

    Mentor Note: thread moved, therefore no template A mass m is placed on a vertical spring and allowed to reach equilibrium, whose level is ##e_0## below the original level of the spring before placing the mass. It is then pushed downwards such that it is now a distance ##x_0## below the...
  2. yrjosmiel

    Maximum delta-v of a rocket engine

    So I was browsing wikipedia when I encountered: What does this exactly mean? How does one calculate for this? << Adding link to the table >> https://en.wikipedia.org/wiki/Spacecraft_propulsion#Table_of_methods
  3. S

    How many places of maximum loudness?

    Homework Statement the last problem on this page: Homework Equations ##v= \lambda f## The Attempt at a Solution I'm guessing I'm looking for the maximum amplitude in a overlapping wavefront diagram like this? ## v=343m/s \\f=512Hz \\343/512=\lambda=0.67m \\3/0.67=4.5m ## So 4.5 wavelengths...
  4. Muthumanimaran

    What is the Maximum Temperature for a Copper Block at 1000 atm Pressure?

    Homework Statement (a) A block of copper at a pressure of 1 atm and a temperature of 5 degree celcuis is kept at constant volume. If the temperature is raised to 10 degree celcius what will be the final pressure? (b) If the vessel holding the block of copper has a negligibly small thermal...
  5. M

    Calculating the maximum force of object 1 without prefix

    Hi, I am busy now for a couple of days with a physics problem. I am not really into physics, so I hope you can help me out. Its about the maximum force of an object (object 1 in this case). I included an illustration. Homework Statement * The left and right pivot have an max of ten thousand...
  6. C

    Maximum extension of system with two blocks connected by a spring

    Homework Statement Two blocks of masses m, and m2 are connected by a spring of spring constant k. Suppose each of the blocks is pulled by a constant force F Find the maximum elongation spring will suffer and the distances moved by the two Homework EquationsThe Attempt at a Solution the two...
  7. S

    Maximum rate at which energy is stored in a LR circuit

    Homework Statement An Inductor L and a Resistance R are connected in series with a battery of emf E. Find the maximum rate at which the energy is stored in the magnetic field. Homework Equations Energy stored in an inductor : U= 1/2Li2 For a simple LR circuit with a DC voltage source the...
  8. D

    Engineering Calculate the maximum power of the resistor in a circuit

    Homework Statement In an AC circuit of periodic current we know: ##E=6[V]##, ##R_g=50[Ω]##, ##L_g=\sqrt3 [nH]## and ##ω=50*10^9[s^{-1}]##. Calculate: a) All available power of the ##E## b) The resistance of ##R## so that the average power is max c) That average power from part b) Homework...
  9. F

    What is the Maximum Angle of Deflection in a Particle Collision?

    Homework Statement A particle of mass ##M## and speed ##v_1## bumps a particle of mass ##m##, ##(M >m)##, at rest. Find the maximum angle of deflection of ##M## after the bump.The Attempt at a Solution I would like to solve this problem in the reference frame of the center of mass, because it...
  10. E

    Finding the maximum displacement

    Homework Statement I want to find the maximum displacement of block A in the left direction Homework EquationsThe Attempt at a Solution I first found the velocities of both blocks after the bullet escapes with 100m/s by using the impulse-momentum theorem. I then applied the work-energy...
  11. T

    Quadratic equation for maximum compression of a spring

    Homework Statement A 1.2 kg block is dropped from a height of 0.5 m above an uncompressed spring. The spring has a spring constant k = 160 N/m and negligible mass. The block strikes the top end of the spring and sticks to it Find the compression of the spring when the speed of the block...
  12. H

    Maximum weight carried by a specific torque

    Hello, My name is Hugh Carstensen. I am a CSE undergrad at the Ohio State University. I recently secured a position designing and assembling an automated camera-rig for digitization of archival works in the Knowlton School of Architecture. The rig will be powered by a number of small stepper...
  13. P

    How to calculate the maximum RPM of a motor?

    Hello all, Just wondering if there is a mathematical formula that calculates the maximum rpm. If I have a fan that puts out 3 pounds of rotational force at stall speed(completely still) at the end point of a 1.5 ft blade what would be the maximum rpm of this fan with the blade attached. What...
  14. R

    Maximum distance ahead of trooper reached by red car

    Homework Statement A trooper is moving due south along the freeway at a velocity speed of 21 m/s. At time t= 0, a red car passes the trooper. The red car moves with constant velocity 28 m/s. At the instant the troopers car is passed, the trooper begins to speed up at a constant rate of 2 m/s^2...
  15. Mr Davis 97

    Finding the maximum of a product

    Homework Statement If ##A,B,C,D## are positive numbers such that ##A+2B+3C+4D = 8##, then what is the maximum value of ##ABCD##? Homework EquationsThe Attempt at a Solution From AM-GM, I know that the maximum is ##2/3##. However, I want to know exactly what A,B,C, and D must be to take on this...
  16. J

    Maximum height a waitress can push on a glass without it tipping

    Homework Statement I have attached the problem. I will write it out: A waitress attempts to push a glass of water of heigh 15.o cm and diameter of 7.00 cm on a dining table, as shown in the figure. If the coefficient of static friction between the glass and the table's surface is 0.350, what...
  17. T

    What determines the maximum weight an electric motor can lift?

    What determines the maximum amount of weight an electric motor can lift / move for its size? So assuming the electric motor weighs a specific amount, what would be the limiting factor to how much weight it can move / lift for the weight it weighs?
  18. MattRob

    Flight Mechanics - Maximum Cruise Altitude

    So, I was helping someone with some science fiction stuff and got to poking into flight mechanics. So we've got a balance of lift and weight, and drag and thrust. The speed at which thrust and drag cancel determines the speed of flight. The speed of flight determines lift, and lift must cancel...
  19. C

    B G-forces exposed during maximum perfomance Takeoff (Heli)

    Hello Folks I'd like to know if anyone of you guys know how to calculate the gforces in a glider (in this case helicopter) during maximum performance acceleration? Tonight I had a very serious discousion with a relative of mine who doubt that it's possible to accelerate from 0 to 140 kts within...
  20. ciao_potter

    Maximum Distance Traveled with Constant Propulsion

    Lets say that we have a rocket positioned at a certain angle with respect to the horizontal. The rocket is fired, with a constant propulsion force of . Assume that the rocket has a constant mass of kg (the gas used to propel the rocket is negligibly small). What is the optimal angle with...
  21. C

    Projectile motion -- how long does it take the projectile to reach maximum height?

    Homework Statement A projectile was launched at 70 m/s at an angle of 45 degrees above the horizontal, how long does it take the projectile to reach maximum height? Homework Equations Vyo= initial vertical velocity Vo=initial velocity The Attempt at a Solution I tried using the...
  22. Pushoam

    Maximum distance the car accelerates in a circle without skidding

    Homework Statement Homework EquationsThe Attempt at a Solution At distance s, the speed of the car is v. $$ v^2 = 2wτs$$ $$\frac { mv^2} R ≤ kmg$$ Let's denote the maximum distance covered without sliding is smax. $$\frac { m2wτsmax} R = kmg$$ $$ smax = \frac {kgR} {2wτ}$$ Is this correct...
  23. A

    I Max and min values -- Finding them in a data set

    I have some data collected from experiment and I want to calculate the max and min values for this data. Please note that these data not a result of function. What is the best mathematical way to get the max and min without just picking them by directly observation.
  24. R

    I Where is a planet's gravity maximum?

    An object approaching Earth (or any planet) experiences increasing gravity as it gets nearer. However, If the object could continue until reaching the center it would find itself again in a net zero gravity field. At what point will it experience the maximum amount of gravity?
  25. curiosity colour

    Solve SHM: Max Acceleration | Physics Homework

    Homework Statement *Forgot to mention that this is a SHM question in the title Which of the following statements about an object that which perform an Simple harmonic motion is true? A) the acceleration is maximum when the velocity is maximum B) the acceleration is maximum when the displacement...
  26. T

    I Is the Maximum of a Continuous Function Proven in This Content?

    the function is continuous, prove f have max in
  27. Quantum Velocity

    I What is the maximum triangle?

    I know that if a triangle have it edge // to each orther then it í the maximum triangle. Pls explain i don't understand hơ thí even possible
  28. BenAS

    Help calculating maximum loads

    So I am trying to solve a problem, I’ve done a simple solution but I want a more comprehensive answer and don’t know how to do the math. The problem involves climbing anchors and the difference between max loads of an equalized vs non equalized anchor. The two different situations, I’ll try to...
  29. T

    Maximum Amplitude of Sound Wave?

    This animation demonstrates a longitudinal wave by means of moving bars. I realized that if we increase the amplitude of the wave, the bars will eventually start passing through each other, which sounds (no pun intended) like an unphysical scenario. Does this mean that there is a cap, a...
  30. Const@ntine

    Diffraction Barrier-Class of Maximum?

    Homework Statement A Diffraction Barrier has 4200 openings per 1cm. A screen stands 2.00 m opposite of the Barrier. Say that for a certain class m, the maximums that correspond with two different wavelengths (589.00 nm & 589.6 nm) abstain from each other by 1.54 mm. What is the value of m...
  31. Muthumanimaran

    Finding the maximum value of current

    Homework Statement galvanometer with 50 divisions on the scale requires a current sensitivity of 0.1 m A/division. The resistance of the galvanometer is 40Ω. If a shunt resistance 0.1 Ω is connected across it, find the maximum value of the current that can be measured using this ammeter...
  32. F

    Find the gear ratio for maximum angular acceleration

    Homework Statement A constant torque is applied to a pinion which has a moment of inertia of I_m. The pinion(A) drives two gears, one (B) which is connected to a mass which has a moment of inertia = I_m and the other(C) is connected to a mass which has a moment of inertia = 2I_m. The gear...
  33. moriheru

    Finding the maximum value of a sum involving several parameters

    Homework Statement Given that a1+a2+a3+... +a7=1 and that all aj is smaller than 1 and greater than 0 and variable , find the maximum value of 6a1+5a2+4a3+...+ a6 Homework Equations no further constraints The Attempt at a Solution I have no idea how to solve this problem specifically, but I...
  34. S

    How to calculate maximum gearbox input torque

    I am a bit confused by a customer and their request to know what the maximum torque he can apply to a gearbox when the motor input speed is 258rpm. The motor is a 2HP brakemotor, 1750rpm at 60Hz, 460VAC 3phase, 1.65 amps motor tested. The gearbox has a 200:1 ratio rated for 0.093HP with an...
  35. K

    Maximum, minimum, and continuity

    Homework Statement Theorem 3 that i will give in the attempt at a solution talks about a closed interval, here it's open Homework Equations Continuity: $$\vert x-c \vert < \delta~\Rightarrow~\vert f(x)-f(c) \vert < \epsilon$$ $$\delta=\delta(c,\epsilon)$$ The Attempt at a Solution
  36. E

    Experimenting with Windings: Maximum Voltage Output?

    I attach an image of something I am experimenting with. The picture itself (and added text) should be self-explanatory. 1) Which way should my windings (clockwise or counter-clockwise) go around P1; P2; P3 & P4 for maximum voltage (V) ? [ 1 Ø ] [ 1 x single enamelled copper conductor ] [...
  37. M

    Computation of maximum pressure in heated closed vessel

    I have a relatively simple design problem but my memories of thermodynamics are very rusty and I can't figure it out on my own. To make it short, I want to put a mix of solid, water and air in a 500mL pressure vessel and heat it all up to 250'C for several weeks. T and P are at room conditions...
  38. T

    VSD for induction motor maximum current

    Hi, I'm trying to ascertain when you're driving an asynchronous motor with VVVF or whatever else a VSD uses, when do you draw the most current? For instance, say you're talking about a train/tram: I would have thought intuitively that since power = torque / angular speed, that starting up, to...
  39. G

    The relation between the energy minimum and entropy maximum

    Hi. This is the problem 5.1-1 from the second edition of Callen's Thermodynamics. It says Formulate a proof that the energy minimum principle implies the entropy maximum principle. That is, show that if the entropy were not maximum at constant energy then the enrgy could not be minimum at...
  40. K

    Is there a maximum limit for particle histories in MCNPX input files?

    Hi, I would like to know if there is any maximum limit for number of particle histories can be used in mcnpx input file. Thank you. Regards,
  41. B

    Maximum work done in a Carnot Cycle

    Given that in a Carnot Cycle the two adiabatic processes are essentially equal and opposite in magnitude the total work done by the cycle is in the two isotherms. The total work of the system is generally given as -NR(Th-Tc)ln(Vb/Va). Does this mean that the work done by a monatomic ideal gas is...
  42. R

    Maximum angular velocity of disc skidding across surface

    Homework Statement coefficient of kinetic friction between the disk and the surface is 0.42 gravity = 10.6 m/s disk mass = 1.75x10^9 the skid marks are 1280m long, This is due to the fact that uneven friction had set the saucer in very slow rotation around its principal axis. By...
  43. E

    Maximum area for inscribed cylinder

    Homework Statement Inscribe in a given cone, the height h of which is equal to the radius r of the base, a cylinder (c) whose total area is a maximum. Radius of cylinder is rc and height of cylinder is hc. Homework Equations A = 2πrchc + 2πrc2 The Attempt at a Solution r = h ∴ hc = r - rc A =...
  44. W

    Maximum value of gain if tranistor not to be saturated

    Homework Statement Homework EquationsThe Attempt at a Solution I don't know how to calculate part C) of the question. I'm unsure what saturation of a transistor refers too.
  45. P

    I Weak Maximum Principle Explained

    Hello,I am reading the link http://math.mit.edu/~jspeck/18.152_Fall2011/Lecture%20notes/18152%20lecture%20notes%20-%204.pdfSays : w_t-D w_{xx}=f with f<0w at \bar{Q}_T has its maximum in \partial_p {Q}_T. If w is strictly negative at \partial_p {Q}_T then also is strictly negative in...
  46. F

    Maximum current through a capacitor

    Homework Statement A 2200 µF capacitor is charged to a potential difference of 12 V and then discharged through an electric motor. The motor lifts a 50 g mass through a height of 24 cm. The capacitor is charged to 12 V again and then discharged through a 16 Ω resistor Determine the time...
  47. S

    I How do I normalise my data to a maximum of 100?

    I have this set of data (in the attached image) and I'm trying to normalize the counts at each angle to a maximum of 100. I'm not sure how to do it though. Any tips would be much appreciated. I have the mean and std dev for each count at each angle. I don't really know what to do from here...
  48. E

    Find maximum acceleration given the displacement equation

    Homework Statement Given: x=9sin2t +16cos2t+100 The problem asks me for the maximum acceleration and the maximum velocity. Homework Equations dx/dt=v dv/dt=a The Attempt at a Solution The problem asks me for the maximum acceleration and the maximum velocity. To find the maximum velocity, i...
  49. J

    I Argument that a maximum density Universe expands linearly

    The Friedmann equation for a spatially flat Universe is given by $$\Big(\frac{\dot R}{R}\Big)^2=\frac{8 \pi G}{3}\rho$$ where ##R(t)## is the proper radius of some spherical volume with us at its center. Let us assume that there is a mass ##M## inside this spherical volume of radius ##R##. The...
  50. F

    I Maximum likelihood w/ histogram, zero probability samples

    I'm trying to replicate a machine learning experiment in a paper.The experiment used several signal generators and "trains" a system to recognize the output from each one. They way this is do is by sampling the output of each generator, and then building histograms from each trial. Later you...
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