Maximum Definition and 1000 Threads

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. S

    Maximum angle between resultant and original vector

    Homework Statement Two vectors of magnitude 5 units and 3 units are added such that the angle between the resultant and the vector of magnitude 5units is maximum. Find this angle. Homework EquationsThe Attempt at a Solution Knowing that the resultant vector makes a smaller angle with a...
  2. Jazmin Urioste

    I Finding Maximum Strain with Cantilever Beam

    Hello, I am trying to establish what the moment of inertia is for this cantilever beam as well as the maximum strain. General formals preferred. Thank you
  3. F

    Maximum load platform can withstand

    Homework Statement A platform is supported by a rectangular plastic tank below . When there's no external load act on it , it oscillate on the water surface with amplitude 0.05m . When it's in equilibrium , the water reaches 0.07m of the height of tank submerged in water. P/s : the tank has a...
  4. P

    What is the Maximum Height Achieved by a Soccer Ball Kicked at a 45° Angle?

    Homework Statement A soccer ball is kicked at a 45° angle. If the ball is in the air for 3 s, what is the maximum height achieved Homework Equations y=viy + 0.5 x ay x t The Attempt at a Solution i used trig to get the vertical and horizontal components i got 2.2 for each side (as there the...
  5. I

    Current at maximum power - PV cell

    Hello there ! I got question regarding PV cell. The current at maximum power Im calculated from current-voltage characteristic doesn't equal to the one calculated from P(Ushunt, as you can see in the attached picture. http://prnt.sc/b864hx Furthermore, the Im from P(U) characteristic is about...
  6. A

    The speed of a projectile when it reaches its maximum height

    Homework Statement The speed of a projectile when it reaches its maximum height is one-half its speed when it is at half its maxi- mum height. What is the initial projection angle of the projectile? Homework Equations Vf2 = vi2 + 2axThe Attempt at a Solution I know that the speed at the top...
  7. Q

    Finding the maximum load capacity of a shelf

    I have been asked to provide an estimate of the maximum load capacity of a shelf that would be 4.5ft by 1ft The information I know is as follows: Bending Stiffness=1750 Nm Area of shelf= 4.5ft by 1ft= 4.5 ft^2=0.41806368m^2 Thickness of shelf= 18mm I need either the equations I could use to...
  8. G

    Maximum power factor of three phase receiver

    Homework Statement Given symmetric three phase system (see attachment) of phase voltages with angular frequency \omega=100 rad/s, R=5\omega L=100\Omega. Find capacitance of capacitor C such that power factor of three phase receiver has maximum value. Homework Equations Power factor is given by...
  9. RoboNerd

    Question on finding maximum magnitude of acceleration

    Homework Statement An object is moving in the xy-plane according to the equations x(t) = 3sin(3t) and y(t) = 4cos(3t). What is the maximum magnitude of the particle's acceleration? 1) 5 m/s22) 15 m/s23) 30 m/s24) 36 m/s2 [the accepted answer]5) 45 m/s2 Homework Equations x(t) =...
  10. I

    Calculating the maximum shear stress in a shaft

    Homework Statement Homework Equations Torque = Force x Distance Shear stress = Force/Area 3. The Attempt at a Solution I know how to do this question as I've seen the mark scheme. However, initially I did it wrong. What I did was as follows: Torque = Force x Distance therefore...
  11. A

    What is the Maximum Speed Needed to Avoid a Collision?

    Homework Statement Magna is traveling at 110 kph, and realizes Commodore in front of him is traveling at 80kph. To avoid a collision, what is the max speed the Magna can have as it reaches the commodore? Homework EquationsThe Attempt at a Solution I am not sure how to approach this.
  12. JulienB

    Contraction, integral, maximum norm

    Homework Statement Hi everybody! Here is another problem about contraction and Banach fixed-point theorem that I don't get: The function ƒ: C([0,½]) → C([0,½]) is defined by: [f(x)](t) := 1 + \int_{0}^{t} x(s) ds ∀ t∈[0,\frac{1}{2}]. Is ƒ a contraction with respect to the norm || ⋅ ||∞? If...
  13. Albert1

    MHB How to Find the Maximum of the Function f(x)=12x-32+24√(9-3x), for x≤3?

    $f(x)=12x-32+24\sqrt {9-3x}, x\leq 3$ find $max f(x)$
  14. JulienB

    Maximum norm and Banach fixed-point theorem

    Homework Statement Hi everybody! I have a math problem to solve, I'd like to check if I understand well the Banach fixed-point theorem in the case of Euclidean norm and how to deal with maximum norm. Check if the following functions ƒ: ℝ2 → ℝ2 are strictly contractive in relation to the given...
  15. Evangeline101

    What is the maximum height of a spring toy launched at an angle?

    Homework Statement A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. What is the maximum height reached by the spring toy? Homework Equations Δ[/B]dv = v1Δt + 1/2aΔt2The Attempt at a Solution [/B] Calculate time: Δt = 2.3 m/s / 9.8m/s2 = 0.23 s Now...
  16. H

    Finding Maximum Number of Interference Maxima?

    Homework Statement Light of wavelength λ = 535 nm shines through two narrow slits which are 670 μm apart. What is the maximum number of interference maxima which could conceivably be observed (assuming that diffraction minima do not extinguish them and the screen is arbitrarily large)?Your...
  17. whatphysics

    Using differentials to estimate the maximum possible error

    Homework Statement Consider a closed rectangular box with a square base of side 3cm and height 5cm. If the side is measured with an error at most 0.02cm and the height is measured with an error at most 0.01cm, use differentials to estimate the maximum possible error in computing the volume of...
  18. Monsterboy

    Maximum height over which water can be siphoned

    Homework Statement A student siphons water over a 8.5 m high wall at sea level. She then climbs to the summit of a mountain (elevation 4390 m , atmospheric pressure =58.5 kPa) and attempts the same experiment. Comment on her prospects for success. Homework Equations Bernoulli's equation...
  19. K

    Find the maximum thermodynamic efficiency

    Homework Statement If an engine operates between 250°C and 25°C, what is its maximum thermodynamic efficiency?Homework Equations Ec=1-Tc/Th The Attempt at a Solution 1-25/250 =90% or 1-(25+273)/(250+273) =43% In this question,which one should I use K or ºC ? thank you
  20. W

    Maximum value of Von Neumann Entropy

    Homework Statement Prove that the maximum value of the Von Neumann entropy for a completely random ensemble is ##ln(N)## for some population ##N## Homework Equations ##S = -Tr(ρ~lnρ)## ##<A> = Tr(ρA)## The Attempt at a Solution Using Lagrange multipliers and extremizing S Let ##~S =...
  21. S

    Determine the absolute maximum bending stress of the beam.

    Homework Statement If w = 74 kN/m , determine the absolute maximum bending stress in the beam in MPa. Homework Equations I'm not too sure how to go about my calculations. Please help! The Attempt at a Solution I = [(1/12)*(200*256^3)] - [(1/12)*(192*250^3)] = 29.62*10^6 F = 74*24*1000? [/B]
  22. I

    What is the maximum induced EMF in a rotating contour near a straight wire?

    Homework Statement In the very long wire conductor as shown on the picture , flows a current magnitude I. Near the wire there is a square shaped contour , with length a ,which rotates around its axis a constant angular velocity. Axis of square contour and a straight line conductor are...
  23. R

    Maximum acceleration of a spring

    Homework Statement A spring with a spring constant of 5.0 N/m has a 0.25 kg box attached to one end such that the box is hanging down from the string at rest. The box is then pulled down another 14 cm from its rest position. Calculate the maximum height, the maximum speed, and the maximum...
  24. lep11

    Prove f has maximum value in R

    Homework Statement Let f: ℝ→ℝ be continuous function such that f(x) approaches 0 when x---> -∞ and f(0)=2. In addition, f is decreasing when x≥3. Prove f has a maximum (greatest value) in ℝ. Homework Equations Theorem: If function f is continuous on a closed interval [a, b], then f has maximum...
  25. M

    Max Photon Energy: Planck Length Lower Limit?

    Planck length is ~ 1.6\times 10^{-35} meters. Does this mean that this may be a lower limit on meaningful wavelength and therefore upper limit on energy?
  26. JulienB

    Finding Extrema of a Set: A Derivative Approach

    Homework Statement Hi everybody! It's kind of the first time that I try to solve this type of problem, so I'd like to see what you guys think about it and if I am heading in the right direction: Examine if the set {(x2 + x + 1)/(x2 + 1) : x∈ℝ} has a maximum and/or a minimum, and calculate...
  27. twiz_

    Maximum voltage from blowing through small turbine?

    If I had a turbine roughly 2 inches in diameter (4-5 blades), where the housing for the blades is about one inch wide (meaning the axle is 1"), what would be the estimated voltage I could produce if I were to use my lung power in one complete exhale through the input? That is, if there were...
  28. anemone

    MHB Max Value of a: Positive Integer Solutions

    If both $a$ and $\sqrt{a^2+204a}$ are positive integers, find the maximum value of $a$.
  29. scotty c

    Maximum air velocity through a hole

    this should be easy. suppose i have a very large spaceship holding a tremendous volume of air at 14.7psi with a density of .0023769 slug/ft^3. i put a hole in the side of my spaceship that is 6" in diameter which vents to the vacuum of outer space. what is the velocity of the escaping air? i did...
  30. R

    Calculate Maximum Load of a U Bracket

    I have a hydraulic cylinder that can lift up to 3 metric tons and I want to attach it to an arm. The bracket is in a rigid U shape (right angles only, no round corners), with a round pin going through it. At first I thought it'd be a simple bending stress calculation, but there is a giant hole...
  31. blueray101

    The maximum deformation of the ball?

    Homework Statement Part 1: I've worked out part 1 already. The answer is 4650m/s^2 A ball travels vertically downwards until it hits a concrete floor with speed 22.7-m/s. It then bounces vertically upwards at 10.8-m/s. Examination of a high speed video shows that the collision took 7.2-ms...
  32. Jess Karakov

    Trapezoidal Rule: Maximum error in approximation?

    Homework Statement Suppose that T4 is used to approximate the ∫ from 0 to 3 of f(x)dx, where -2 ≤ f ''(x) ≤ 1 for all x. What is the maximum error in the approximation? Homework Equations |ET|≤ (K(b-a)^3)/(12n^2) The Attempt at a Solution So I know how to find the error of the trapezoidal...
  33. A

    What is the maximum charge on plates when dielectric removed

    Homework Statement A capacitor with two parallel plates of area 88.5 cm2 and nylon (dielectric strength 14 MV/m) inserted between them breaks down when a potential difference of 5.80 kV is applied. What is the maximum charge the plates will hold when the nylon is removed and the space filled...
  34. N

    Maximum Error Using Differentials

    Homework Statement 2 adjacent sides of a parallelogram measure 15ft and 10ft w/ max errors of ±0.1ft angle is 45° w/ max error of ±0.5° What is the maximum error in the calculated value of the area or the parallelogram? Homework Equations A = area = xysinθThe Attempt at a Solution x = 15ft...
  35. U

    Structural engineering question -- maximum load taken by beam

    dear all , My question is what is the maximum load taken by beam of UB 610 x 229 x 125Kg/m for a span of 5 mtr? its supported on both side by anchoring on concrete beam.
  36. M

    MHB Finding the Maximum Value of n for a Given Equation

    What is the Largest possible value of n such that there is a multiple of 4 less than n^2 but greater than n^2 + 2016/n^2 ?
  37. Elena14

    Maximum kinetic energy in projectile motion

    Finding the maximum kinetic energy in a simple parabolic projectile motion requires us to find the maximum velocity. I know that the velocity will be maximum at two points, the point of projection and point of return. So there must be two points where the kinetic energy is maximum. But my...
  38. DaTario

    Maximum number of layers of immiscible of fluids

    Hi All, What is the maximum number of layers of immiscible fluids in nature. Is seems intuitive to me that this limit exists. for the sake of definiteness, let' s consider usual laboratory"s condition of temperature and pressure. Best wishes, DaTario
  39. avito009

    Is 2.5 m maximum length of lintel? Why?

    I read this in Gordon's book "Structures or why things don't fall down". I read that the maximum length of lintel should be a maximum of 2.5 metres. Why? What if its more?
  40. T

    Maximum height water can be projected onto a wall

    Homework Statement H3-1 Determine the maximum height on the wall to which the firefighter can project water from the hose if the speed of the water at the nozzle is 20 m/s. The firefighter stands 18 m away from the wall and holds the nozzle 1.2 m above the ground. Homework Equations The...
  41. L

    Binding energy/position of maximum energy value

    Homework Statement The binding energy of the ion H2+ is -16.3 eV at the equilibrium separation 0.106 nm. The Hellman-Feynman theorem states taht the force between the nuclei in a molecule can be calculated from the electrostatic repulsion between the nuclei and the electrostatic attraction of...
  42. C

    Maximum bending Moment and Maximum Shear Stress Question

    Is the maximum bending moment and maximum shear stress an absolute value? For example, when drawing out a bending moment diagram say if I get -400 kNm at one point and 300 kNm at a different point. If these values are the maximum/minimum points on my diagram would 400 kNm be considered as a...
  43. K

    Mathematica FindMaximum function in Mathematica

    I recently plotted a piecewise function: Plot[Piecewise[{{1 - Exp[-.002*t], 0 <= t < 120}, {-Exp[-.002*t] + Exp[-.002*(t - 120)], 120 <= t}}], {t, 0, 5000}, PlotRange -> {0, 0.25}] I then defined the function which I am calling q[t_] as follows: q[t_] := Piecewise[{{1 -...
  44. K

    What is the maximum distance for a receiver to pick up a 12.5-MHz signal?

    Homework Statement Points A and B are 56.0 m apart along an east-west line. At each of these points, a radio transmitter is emitting a 12.5-MHz signal horizontally. These transmitters are in phase with each other and emit their beams uniformly in a horizontal plane. A receiver is taken 0.500...
  45. K

    Maximum Torque in Dipoles (electrostatics)

    In a --specifically uniform electric field-- (I may be wrong here) my understanding is that the dipoles will result in no net dipole force (due to cancelling out) but there will actually be a net torque experienced about the center. This torque will be trying to turn the dipole so the moment, p...
  46. B

    What Is the Maximum Initial Velocity of a WW2 German U2 Rocket?

    Homework Statement A German U2 rocket from WW2 had a range of 300km, reaching a maximum height of 100km. Determine the rocket's maximum intial velocity. X component variables: di=0, df=300, a=0, time=9, vi=? Y component variables: a=-9.8, vf=0, vi=?, di=0, df=100, displacement=100, Note: For...
  47. D

    Maximum Likelihood and Fisher Information

    Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...
  48. D

    Find MLE of θ: Maximizing Likelihood fxn

    Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...
  49. L

    Maximum ratio of calcium, atp hydrolysis

    Hello, 1-The standard free energy associated to the hydrolysis of one ATP mole is -31 kJ. What would be the energy when [ATP]=5mM , [ADP]=0.5mM and [Pi]=1mM 2-Calculate the free energy required to move 1 mol of Ca2+ ions from the outside of the cell (where [Ca2+] = 10-3) to the inside (where...
  50. P

    Calculating Maximum Pressure for T6 Aluminium Cylinder

    Hi guys, The imagine the picture attached is a cross section of a cylinder. How would I work out the maximum amount of pressure this can be exposed to before the metal shears off at the location labelled "2mm thick"? Lets say the following material is used: T6 Aluminium Ultimate Tensile...
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