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. anemone

    MHB Find maximum integral value of k

    Find the maximum integral value of $k$ such that $(k-4)(x^2+x+1)^2-(k-3)(x^2+x+1)(x^2+x+2)+(x^2+x+2)^2=0$ has at least one real root for $x$.
  2. B

    Hi there, i have a question on maximum current inputs of IC

    hi there..i have a question...back at my work, we have a power supply which have a variable current and a variable voltage...my senior said, he have a ic board to check, and then he uses a 5 volt supply with unknown current on it to power up this board, he then claims that you can supply the...
  3. Calpalned

    Finding the maximum value of a gravitional force field

    Homework Statement Two identical particles, each of mass m are located on the x-axis at ## x=+x_0 ## and ## x = -x_0##. At what point (or points) on the y-axis is the magnitude of ##\vec g ## a maximum value and what is its value there? Homework Equations Formula for gravitational field...
  4. S

    Find maximum wavelength using minimum wavelength and frequency difference

    Homework Statement A radar receiver can be tuned to detect signals are different wavelengths. If the frequency difference between the minimum and maximum wavelength is 10 GHz and the minimum detected wavelength is 4910µm. What would be the maximum wavelength? Homework Equations λƒ=c The...
  5. W

    Finding the maximum displacement of a vertical spring using energy conservation

    Homework Statement A mass of 0.36kg hangs motionless from a vertical spring whose length is 0.8m and whose unstretched length is 0.51m. Next, the mass is pulled down to where the spring has a length of 1.09m and given an initial speed upwards of...
  6. julianwitkowski

    Single Slit / Wavelength / Central Maximum

    Homework Statement A laser emitting light with a wavelength of 560 nm is directed at a single slit, producing an interference pattern on a screen that is 3.0 m away. The central maximum is 5.0 cm wide. Determine the width of the slit. I have two ideas of the answer but I'm not sure which is...
  7. anemone

    MHB Find Maximum $(xyz)^2$ Given $x+y+z=0, x^2+y^2+z^2=2015$

    If $x,\,y,\,z$ are three real numbers such that $x+y+z=0$ and $x^2+y^2+z^2=2015$, find the maximum of $(xyz)^2$.
  8. H

    Minimizing the maximum bending moment

    Homework Statement The question is asking us to minimize the maximum bending moment by changing l3. l1=3(m) l2=6.5(m) l4=12(m) P1=1200(KN) P2=2300(KN) P3=410(KN) and we know that obviously, 6.5<l3<12 Homework EquationsThe Attempt at a Solution We made relevant cuts and acquired the equations...
  9. A

    Maximum Torque Calculation for a Given Force and Angle

    Homework Statement 2. Homework Equations [/B] I was given this info r=1.5 m d=3 m F= 50 angle= 110 degreesThe Attempt at a Solution T=Fsin T= (1.5)(50)sin(110) T=70 N I attempted the solution^ to get (maximum) torque.
  10. J

    Maximum impact force that a cable can withstand

    Homework Statement " A 1100 kg lift is suspended by a series of 24 steel cables of mean diameter 20mm. The cables are attached to the lift top and are arranged so that torsional vibration is minimised.If the cable is manufactured from steel with an elastic modulii of 185GN/m2 and elastic...
  11. K

    Finding the maximum compression of a spring

    Homework Statement A block of mass m1 slides along a frictionless table to the right with a speed of v1. A second mass M2 slides in the same direction with a speed of v2 such that it will collide with m1 which is in front of m2. Say that a spring of stiffness k is attached to one of the masses...
  12. I

    How can I displace the maximum amount of water in a bucket?

    The scenario involves dropping something into a bucket of water. I'm trying to do an experiment where I have to figure out a relationship between the amount of water that leaves the bucket and a certain variable of the object that is dropped. I'm wondering what could maximize the water that...
  13. R

    Maximum and minimum values of a variable capacitor

    Homework Statement A parallel circuit like that in the figure forms the tuning circuit for an AM radio. If the inductor has a value of 8.6×10-6 H, what must be the maximum and minimum values of the variable capacitor if the radio receives frequencies from 590k Hz to 1670k Hz? a) Maximum C? b)...
  14. evinda

    MHB Find Maximum n for Time Constraints: Solving Problems Using f(n) Microseconds

    Hello! (Wave) I am looking at the following exercise: For each function $f(n)$ and for each time $t$ find the maximum size $n$ of the problem that can be solved in time $t$, assuming that the algorithm of the problem requires time $f(n)$ microseconds( 1 microsecond=$10^{-6}$ second) Suppose...
  15. Poetria

    Maximum kinetic friction-combined with a projectile problem

    Homework Statement A cannon at ground level is shooting emergency packets to people stranded on the roof of a flooded building of height H=125 meters. The corner of the building is located a distance D=50 meters from the cannon. It is desired that the incoming packets are flying tangent to the...
  16. G

    Find Maximum Power to Resistor R

    Homework Statement Homework Equations Pmax = ((VTh)2)/(4RTh) Rparallel = (R1R2)/(R1 + R2) KCL ΣI = 0 KVL ΣV = 0 The Attempt at a Solution Okay, so to find RTh, I remove all independent sources and set the "terminals" at R to have a 1A current running through them. Since there is a 30kΩ...
  17. P

    Maximum shear stress on a given plane?

    I want to know the maximum shear stress acting on the y-z face(plane). I already know all 6 stress components: Sxx, Syy, Szz, Sxy, Syz, Sxz. The shear components on the y-z face are Sxy and Sxz, which are orthogonal to each other. Is the maximum shear on this plane simply the greater of the two...
  18. S

    Find the maximum value of this complex function

    Homework Statement Find the maximum value of f(z) = exp(z) over | z - (1 + i) | ≤ 1 Homework Equations |f(z)| yields the maximum value The Attempt at a Solution f(z) = exp(x) ( cosy + i siny) Unfortunately that's all I've got. I've seen examples with polynomials, but not with trigonometric...
  19. E

    Maximum order of essential and natural conditions

    Is there a physical explanation for why when given a differential equation with spatial derivative of spatial order 2m the maximum order of the essential (displacement) boundary condition is m, and the maximum order of the natural (force) boundary condition is 2m-1 for example, the equaiton...
  20. M

    Use Lagrange's method to find maximum.

    Homework Statement Let u = ∂f/∂x and v = ∂f/∂y. Use Lagrange's method to set up the equations necessary for finding the maxium of u^2 + v^2. Homework EquationsThe Attempt at a Solution I know how to minimize and maximize a function that's a subject to another one. I'm not quite sure what the...
  21. M

    Maximum Height of a Thrown Stone with Air Resistance

    Homework Statement A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. Air resistance is proportional to speed, with k=1/128 lb-s/ft. Find the maximum height attained by the stone. Homework Equations None. The Attempt at a Solution Here's...
  22. L

    Obtaining a maximum resistance given a set of resistors

    My gut instinct is that putting all the resistors in series will give max resistance, but I am not sure how to give a more rigorous either mathematical or just in words reasoning why. Or maybe I'm wrong! But it seems like the fraction introduced from parallel won't help In any case, assume all...
  23. O

    Max Power Transfer to Ro: Percentage Explained

    Homework Statement The variable resistor R in the ciruit is adjusted for maximum power to Ro. what percentage of total power developed in circuit is transferred to R. Homework Equations i=V/R The Attempt at a Solution So my goal is to put a "fake" charge across v/2(the dependent source) of 1A...
  24. H

    Maximum separation between blocks on spring

    Homework Statement Two blocks, each of mass m, are connected on a frictionless horizontal table by a spring of force constant k and equilibrium length L. Find the maximum and minimum separation between the two blocks in terms of their maximum speed, vmax, relative to the table. (The two blocks...
  25. A

    Find the acceleration of the system and the maximum force

    Homework Statement There are 3 masses ma= 50 kg, mb= 60kg, mc= 80kg. These masses are connected with a rope that affords a tension of 1000 N. On the mass 3 is applied a force F. Knowing that the tension between A and B TAB= 200 N. a)Find the acceleration b) find the maximal value of the force F...
  26. A

    SHM Question: What is the maximum extension of the spring?

    Homework Statement A 50g block is attached to a vertical spring whose stiffness constant is 9N/m. The block is released at the position where the spring is unextended. What is the maximum extension of the spring? How long does it take the block to reach the lowest point? Homework Equations...
  27. D

    Maximum area of a triangle inscribed in another triangle?

    Homework Statement [/B] Hello! I have this question which I don't quite know how to solve... ABC is an equilateral triangle - the length of its sides equal to (a). DE is parallel to BC 1. What length should DE be to achieve the largest possible area of triangle BDE? 2. What length should DE...
  28. R

    Why the orbitals can contain maximum of 2 electrons?

    why orbitals like s, px, py, pz etc can hold maximum of 2 electrons? Why not some other number?
  29. Albert1

    MHB Find Maximum of $3x-2y$ Given $x^2+4y^2=4$

    $x,y\in R$ and $x^2+4y^2=4$ please find $max(3x-2y)$
  30. M

    Calculating the maximum load that can be carried & extension

    Ive been given a question which I'm stuck on and cannot answer. I've only been able to calculate the maximum allowable working stress and other then that I am stuck on how to answer the following question: A specimen of the same material that was used in the above test (mild steel), had a cross...
  31. T

    Maximum value of two variables

    I'm just doing some geometry and I can't remember how to find the maximum values of two variables in the same equation. Like, if you differentiate the equation partially for one, then again from the beginning partially for the other and add them together or something. The equation is something...
  32. Dennydont

    What is the maximum load the concrete can support?

    Homework Statement A certain type of concrete has a tensile breaking stress of 3.1 MN/m^2, a compressive breaking stress of 37.7 MN/m^2 and a shear breaking stress of 9.4 MN/m^2. A circular pillar of this concrete has a radius of 0.6 m. What is the maximum load it can support assuming that it...
  33. J

    Maximum resistance and power for LED

    Homework Statement You wish to use an LED (D1) which provides essentially zero resistance and is rated to accept either a maximum of 75 mW of power or 30 mA of current. In the following two circuits, what range values for resistor R1 will be acceptable in each case if the voltage provided by V1...
  34. A

    Maximum Interrupting Time - HFW Breakers

    Hi, I need to know the "maximum interrupting time" of the FW/HFW Molded-Case Circuit Breakers (see the attached time-current curves).Thanks
  35. A

    Rocket Maximum Velocity: How to Calculate and Convert Units for Accurate Results

    Homework Statement The whole problem is in picture, but simply it says to find the max velocity of rocket, with those given units. The whole problem is worked out with pounds, but when I try to do it for meter and Newtons I get like 50 times bigger answer. The units : Total Impulse of motor...
  36. 22990atinesh

    Maximum number of comparisons required to merge two sorted files

    Homework Statement Maximum no. of comparisons required to merge two sorted files of length 'm' and 'n' is.. Homework EquationsThe Attempt at a Solution I think m+n-1
  37. D

    How Does Changing Wavelength Affect the Central Peak in Single-Slit Diffraction?

    In my physics book, one of the basic quick quizzes checkpoints asks what happens to the central peak in a diffraction envelope when you decrease the wavelength of light (from 650 nm to 450 nm, for reference). My understanding is that the width of the peak would decrease, while the number of...
  38. O

    Maximum pressure a hull can stand

    Hello, First, please understand that I'm lacking fundamentals in physics and engineering. I'm trying to find the maximum pressure a submarine hull can resist. For the sake of simplicity I'm just considering a tube closed with magical caps that keep a different pressure inside and outside...
  39. Shindo

    Pendulum's maximum momentum?

    Homework Statement A pendulum hung by a string that is 90m (simplicity's sake) can come a maximum of 72m leftward or right ward. Where does it feel it's maximum momentum? m=meters M=mass Homework Equations PE=mgh KE=.5(M)(v)^2 Mv= momentum The Attempt at a Solution My question is: will a...
  40. T

    Why is resistor power maximum in parallel with same value?

    Hello, I want to ask the explanation for this basic problem. So I have 2 resistors in parallel(X and Y) and I want to maximize the power going through the resistor X, by choosing the resistance. This can be achieved only by choosing the same resistance for X, than Y has. Why is this so? I can...
  41. M

    Maximum work can be obtained from reversible process ?

    My book says 'Maximum work can be obtained only from thermodynamically reversible processes,' but why is it so? What is the cause? Actually to me the definition of reversible process is confusing. It says that at each step during the process, equilibrium is maintained. But, let's say,we have to...
  42. D

    Motherboard bus speed physical maximum

    I read somewhere (article, messageboard, i can't find it anymore) that motherboard bus speeds are limited because if the frequency gets too high then the signal will disappear. I guess I understood it to mean that the bus wire will become like and antenna if the frequency is too high. They...
  43. S

    Reflection maximum of material

    Homework Statement A coating of n1 = 1.33 material is to be added to n2 = 1.50 glass, in order to make it "irridescent." a) What is the thinnest layer of material which will have a reflection maximum for normal-incidence light at BOTH 400 and 600 nm (vacuum) wavelength? b) This thickness will...
  44. J

    Maximum vibration speed of a traveling wave

    Homework Statement y(x,t) = (9.00cm)sin((5Πcm-1)x + (3Π rad/s)t - Π/8) There are 11 parts, and I have answered the first 10 (they include velocity of a wave, amplitude, all that good stuff), but I haven't seen anything in lecture or in the textbook that mention finding maximum vibration speed...
  45. O

    Trajectory (Quick Question) -- where would it be maximum speed?

    http://puu.sh/dc1YU/fa1e0f3a6e.png Hey so if we have a trajectory like this, where would it be maximum speed? From what I understand, at the midpoint, v = 0 right? So would the maximum speed be in between the bottom (initial) and the centre of the trajectory (peak), represented by B in this...
  46. D

    Maximum torque for current loop

    Homework Statement A current loops is oriented in three different positions relative to a uniform magnetic field. In position 1, the plane of the loop is perpendicular to the field lines. In position 2 and 3, the plane of the loop is parallel to the field as shown. The torque on the loop is...
  47. R

    Maximum Weight Capacity of Multiple Strings for Hanging Objects?

    if one string can hold a block of 100kg, how much weight can two strings connecting the ceiling and one single point hold a block?? is it 200 kg? if yes, then what about one string connecting the ceiling and one single point of the block two times, three times or more? [im sorry if the grammar...
  48. K

    Calculating maximum shear in a steel beam cantilever

    Problem: I do not know how to approach this problem. For a beam which has two reactions, the shear stress is equivalent to the reaction. I suppose that the stress is calculated using moment some how. But how? For seeing if the beam is allowable stress design compliant, you can use the...
  49. D

    Interpretation of the maximum value of a CDF

    I was watching a youtube video from MIT's open courseware series on probability. A scenario was proposed: Al is waiting for a bus. The probability that the bus arrives in x minutes is described by the random variable X, which is uniformly distributed on the interval [0,10] (in minutes). I...
  50. L

    Finding maximum in interference pattern

    Homework Statement In a three-slit system, the first minimum occurs at an angular position of 5.00°. Where is the first maximum? Homework Equations dsinθ = mλ/N The Attempt at a Solution dsin5° = λ dsinX = λ/3 sinX = 3sin5° X = 1.66° I'm not sure if this is the right equation to find the...
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