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. rsyed5

    MHB Max Volume: Finding Constraints, Dimensions

    So, I have this question, but I have no idea what constraint is and how to find a constraint for the length, height and width... and if i say the square wastage is x, then the width is 80-x but I don't know what the length would be with respect to x... , and how do we determine the dimensions..?
  2. O

    Understand BIL Rating & Maximum Voltage in Equipment

    The difference between BIL rating and Maximum voltage? Like is the BIL voltage the highest it can take in just one instant? how do i know what is the highest continuous voltage a piece of equipment can take? Like for a Cap bank i see a BIL rating but i need to know what's the maximum voltage...
  3. B

    Maximum compression of the spring

    Homework Statement Mass- 0.8 kg Initial Velocity- 3 m/s Spring constant- 500 N/m No friccion Final velocity- 0 Homework Equations What is the maximum compression of the spring? I don't know where or how to start! Please help.
  4. gfd43tg

    Engineering Maximum power transfer in a circuit

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  5. gfd43tg

    Max Power Transfer: Source Voltage & Load Explained

    Hello, I was wondering, why is it that when calculating the maximum power transfer, the source voltage is the thévenin voltage, and not the actual source? What we call the load is arbitrary, no?
  6. D

    Finding the maximum velocity of an object rolling down an incline

    So our teacher explained to us that there is an optimal angle at which a bottle can be rolled down an incline to achieve 'maximum' velocity but I'm not sure how to find the equation to work this out mathematically rather than using just trial and error. I'm pretty sure that it involves...
  7. T

    Impulse and maximum height of a particle

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  8. T

    Engineering Understanding Maximum Power in Circuit: Comparing Load and Circuit Approaches

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  9. J

    Calculate Inductor Maximum Energy: 240V, 50Hz, 4A & Negligible Resistance

    Homework Statement Assuming steady-state sinusoidal ac.A voltage of 240V at 50Hz applied to an inductor yields a current of 4A.Assume negligible resistance.Find inductance, max stored energy. Homework Equations E=0.5Li^2 X=2*pi*f*L The Attempt at a Solution V/I=X Which I...
  10. K

    Kinematics - projectile motion - time to maximum height?

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  11. T

    What is the Maximum Speed at Point Q Without Breaking the String?

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  12. M

    MHB Maximum error for the Lagrange interpolating polynomials

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  13. A

    Van de graff generators maximum voltage

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  14. C

    Maximum possible force exerted on a sail

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  15. A

    Maximum size of a set containing logical expressions

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  16. T

    Maximum power and maximum torque

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  17. D

    Maximum Order Statistic Question

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  18. S

    Maximum height of a projectile thrown from a rooftop

    Homework Statement A man stands on the roof of a building of height 14.6m and throws a rock with a velocity of magnitude 30.8m/s at an angle of 33.2∘ above the horizontal. You can ignore air resistance. Calculate the maximum height above the roof reached by the rock. Homework Equations...
  19. U

    Finding Maximum Value in a Trigonometric Function

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  20. L

    MHB Sos help with maximum and minimum

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  21. C

    What is the maximum volume expansion coefficient of ?

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  22. E

    What is the Optimal Nozzle Exit Pressure for Maximum Thrust in a Turbojet?

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  23. S

    Question to Maximum Likelihood

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  24. B

    Maximum Load question given Safety factor

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  25. xortdsc

    Maximum ionization of free elements

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  26. anubodh

    Maximum Spring Constant for 0.5 cm Length Spring: Does Radius Play a Role?

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  27. B

    Max Conjugate Base: Find pH w/ Sum of pKa's

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  28. A

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  29. A

    Maximum current from a battery

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  30. L

    What is the relationship between stress and load for a 19mm shaft?

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  31. M

    Challenging Find maximum deceleration and speed (not max)

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  32. Saitama

    Finding the maximum acceleration

    Homework Statement Homework Equations The Attempt at a Solution I don't know how to make the equations here. When the balls are penetrating each other, a cavity is being formed due to overlap of the negative and positive charges. The size of this cavity keeps on increasing...
  33. H

    Finding Maximum Speed of an Object - 24.4X9.8

    How to find the maximum speed of the object? Is the maximum centripetal force equal to 24.4X9.8? THX!
  34. NTW

    Endurance & maximum range speeds

    Hello all... I know that it can be derived, from first principles, that maximum endurance and maximum range speeds are related by the factor 3^0,25. But I haven't been able to find a derivation. Could anyone here help...? Thanks in advance...
  35. B

    Derive an equation for the maximum bending moment

    The calculation for the maximum bending moment is to be verified experimentally using a strain gauge bonded to the outer surface of the beam, at the point where the maximum bending moment occurs. Derive an equation which could be used to calculate the bending moment from the measured strain...
  36. anemone

    MHB Finding Maximum Value of an Expression with Respect to $x$

    Hi MHB, I am completely clueless about how to tackle the problem below, given I noticed $y$ increases as $x$ increases, so there is no maximum point over the entire domain for that function, that is for $x \ge 0$, isn't that so?(Tmi) For what value of $x$ is the expression in...
  37. O

    Maximum likehood fonction for LPPL ?

    Maximum likehood fonction for LPPL ?? Can anyone help me to found the the likehood fonction for Log-periodic-power-law ? log(y(t))=A+(B(t-tc)^β )(1+Ccos(wlog(tc-t)+phi)) A,B,C,beta,phi,tc,w : are parameters to be estimeted. thanks
  38. R

    How can I determine the maximum load on a surface?

    I'm trying to determine what equations I can use in order to calculate the maximum load (in pounds) across a sheet of plexiglass. Could anyone help me look in the right direction? This is just a sheet that's 10" x 10" x 1/8", that's held by 4 screws. You see, my project involves placing my...
  39. S

    How to find C and L in maximum current?

    In a RLC circuit, radio waves with different frequency, f, hit the antenna and exert oscillating electric forces on the electrons on the antenna . Thus they act via antenna as individual batteries, each oscillating at their particular frequency f. Suppose R=1000 ohm. What should L and C be so we...
  40. U

    Maximizing Expression Value with Square Roots: Calculus Approach Explained

    Homework Statement The maximum value of | \sqrt{x^4-3x^2-6x+13} - \sqrt{x^4+5x^2+4}| Homework Equations The Attempt at a Solution First of all I'd like to ask a question which always troubles me and that is how do you find max value of any given expression? What clues do you look for...
  41. E

    What is the maximum compression of the spring xmax during the collisio

    Homework Statement A 4.80kg cart has a spring with spring constant 3200N/m attached to its front, parallel to the ground. This cart rolls at 4.40m/s toward a stationary cart with mass 1.60kg . Homework Equations PEspiring = 1/2*kx^2 KE = 1/2*mv^2 The Attempt at a Solution I was...
  42. M

    Maximum amplitude of second order system

    See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.
  43. N

    Find the maximum value?

    Homework Statement Given a=11+/-0.5, b=0.04562+/-0.0001, c=17200+/-100. Find the maximum value of the absolute error in a+2b-c. Homework Equations absolute value of (0.5+2(0.0001)-(-100)=100.5002 11-0.5=10.5 0.04562-0.0001=0.04552 17200+100=17300 absolute value of...
  44. A

    Maximum Mass You Could Boil with 1000 J of Heat (Thermodynamics)

    Homework Statement What is the maximum mass of ethyl alcohol you could boil with 1000J of heat, starting from 18∘C?Homework Equations Q=mcΔT c ethyl alcohol = 2400 J/(kg*K) T boil ethyl alcohol = 78 C = 351 K T starting = 18 C = 291 K The Attempt at a Solution m=Q/(c*ΔT) m= (2400 J)/[(2400...
  45. I

    Maximum velocity of ISON and some other stuff

    Hey I'm trying to find out the maximum velocity that ISON had, should I use Newtonian physics or general relativity equations to find it? What are the values I should assign for mass and distance? Would I need to use differential equations because ISON melted? I don't want anyone giving me the...
  46. W

    Sum of all possible products when each product has a maximum

    Hello I have a set of sets of real numbers greater than 1. Each set can have a different quantity of numbers. Set A1 {a11, a12,...a1m1} Set A2 {a21, a22, ..., a2m2} ... Set AN {aN1, aN2, ..., aNmN} If I want the sum of all possible products that have one element from each set, that's...
  47. J

    Calculating maximum bending stress in an I beam?

    Hello all, I am confused on how to calculate the maximum bending stress in an I-beam. I found the maximum deflection in each beam where the load is placed at the center of the span. I also know all the cross-sectional dimensions of the I-beam. Is it now possible to calculate it? Thanks
  48. S

    Maximum theoretical and experimental stress in T-beam.

    Homework Statement 1. Take dimensions of the beam (B, D, web and flange thickness, L) – T- cross section 2. Take the beam span geometry and material properties from the instrument 3. Ensure the beam and load cell are properly aligned and apply a positive (downward) preload to the beam of...
  49. O

    Angle at Maximum Height

    Homework Statement the initial velocity of a projectile is 150 m\s .the angle between the velocity vector and the trajectory at the projectile's maximum height is a) 90 b) 45 c) zero d) 63.1 e) 36.9 Homework Equations Vox= vx = Vocosθ Vy = Vosinθ-gt Range (R) = (vo)^2*sin(2θ)/g...
  50. R

    Max Speed of Car: 80m Track & .40 Coeff of Friction

    Homework Statement "what is the maximum speed at which a car can safely travel if the radius of the track is 80.0 m and the coefficient of friction is .40" friction is providing the force and the track is flat and circular. Homework Equations the equations that we've been using in class...
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