Minimum 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. Mr Davis 97

    Minimum time for rowing across a river and running

    Homework Statement In hot pursuit of a suspect, Agent Logan of the FBI must get directly across a 1200m wide river in minimum time. The river's current is 0.80m/s, she can row a boat at 1.60m/s and she can run 3.00m/s. Describe the path she should take (rowing + running along the shore) for the...
  2. Mr Davis 97

    How Fast Can Electro-Fiasco I Travel 1 km from Rest?

    Homework Statement A sportscar, Electro-Fiasco I, can accelerate uniformly to 100 km/h in 3.5 s. Its maximum braking rate cannot exceed 0.7g. What is the minimum time required to go 1 km, assuming it begins and ends at rest? Homework Equations SUVAT equations The Attempt at a Solution I think...
  3. M

    Minimum velocity for a surfer to catch a wave

    Hi, I have a question about surfing, how fast must a surfer be traveling (paddle velocity) in order to catch a wave? I took the approach to consider the surfer in the wave's frame of reference, then supposed that the surfer would be 'caught' by the wave if the surfer's kinetic energy was less...
  4. haushofer

    Hamilton's principle and minimum potential energy

    Dear all, I was wondering what exactly the correspondence/relation is between Hamilton's principle (extremizing the action gives the allowed configurations) and the fact that a system wants to configurate such as to minimize its potential energy. Is there any? Somehow I can't find a decent...
  5. JulienB

    Show that grad f(x) = 0 when x is a local minimum of f

    Homework Statement Hi everybody! I'm preparing a maths exam and I unsure how to answer this question: What is a local extremum of a function ##f: \mathbb{R}^2 \to \mathbb{R}##? Explain why ##\nabla f(x) = 0## when ##x## is a local minimum of ##f## and ##f## is continuous and differentiable...
  6. A

    Minimum distance required to reach maximum velocity.

    Hi there! I have a basic question here, hopefully someone can brush physics up for me. I have a motor that is capable of max velocity of 5000°/s, and max acceleration of 30000°/s². What is the minimum distance that the motor need to travel before it reaches that max velocity? Can it make it in...
  7. A

    Minimum distance between bomb and shell

    1. Prolem Statement:- An aircraft is flying horizontally with constant velocity = ##200 m/s##, at a height = ##1 km## above the ground. At the moment shown, a bomb is released from aircraft and the canon- gun below fires a shell with initial speed = ##200 m/s##, at some angle #\theta#. 1)For...
  8. T

    Maximum and minimum transverse speeds at an antinode

    Homework Statement Adjacent antinodes of a standing wave on a string are 15.0cm apart. A particle at an antinode oscillates in simple harmonic motion with amplitude 0.850cm and period 0.0750s. The string lies along the +x-axis and is fixed at x = 0. the speed of the two traveling waves are...
  9. R

    Calculating Minimum Diameter for Steel Pin w/ Partial Uniform Load

    I'm a bit rusty on partial uniform loading on a pin. I want to find the minimum diameter a cold rolled steel pin has to be using a factor of safety of 2 with a loading of 25000 lbs. The pin in the picture is welded between two plates (the right plate bends in and is welded to the left plate...
  10. M

    HVDC - Current Source Converter - Minimum DC Power flow

    Hello, I was reading about the differences between Current Source Converters and Voltage source converters. One main difference was that Current source converters need to have a minimum DC power flow of 5-10% while VSC do not have a min flow requirement. It was also called a deadband. Why is...
  11. Albert1

    MHB Find Min Value of $(s-a)^3+(s-b)^3+(s-c)^3$ for $\triangle ABC$

    $a,b,c$ are lengths of $\triangle ABC$ if: $(1) :s=\dfrac {a+b+c}{2}$, and $(2) :$ the area of $\triangle ABC=1$ find the minimum value of $(s-a)^3+(s-b)^3+(s-c)^3$
  12. K

    Sound frequency from distance b/w first minimum and maximum

    Homework Statement Two speakers are arranged as shown. For this problem, assume that point O is 12 m along the center line and the speakers are separated by a distance of 1.5 m. As the listener moves toward point P from point O, a series of alternating minima and maxima is encountered. The...
  13. Patrick Farnworth

    Classical Further reading after Theoretical Minimum

    Hi, I've just finished secondary school and am keen to learn some physics before going on to college. As part of this I've just finished reading 'The Theoretical Minimum' by Leonhard Susskind and George Hrabovsky. The book was a really helpful introduction to classical physics and the maths...
  14. Marcelo Rodrigues

    Glass vacuum chamber minimum thickness

    Hello! I am designing a vacuum chamber made of a vertical glass cylinder free of contact from any other structure, except by the top and bottom where aluminum disks seal the device. Temperature is the same inside and outside. I found on several books the following formula for the hoop stress...
  15. Albert1

    MHB What Is the Minimum Value of $f$ with Given Conditions?

    find minimum value of $f$ given : $(1)a,b,c,x,y\in R^+$ $(2)x+y=c$ $(3)f=\sqrt {a^2+x^2}+\sqrt {b^2+y^2}$ find :$min (f)$
  16. S

    Bernoulli equation related to minimum pressure inside train

    Homework Statement The train is traveling in a gallery at ##v=70 km/h##. Outside air is not moving and pressure is ##p_0=101325 Pa## and temperature ##T=283 K ##. The area of the face of the train is ##A=9 m^2##. Determine the minimum area of the section of the gallery such that the pressure...
  17. Cleo James

    Minimum Vo for a hoop to get to the top

    Homework Statement part(b) and (c) Homework Equations Conservation of momentum Conservation of angular momentum Conservation of mechanical energy The Attempt at a Solution So first I thought that I could do it by just using the conservation of mechanical energy, but then I realized that since...
  18. 1

    Sub $100 Low minimum High Voltage DC probe (3kV minimum)?

    Hi I'm looking for a suitable high voltage prob for my research project. I'm in contact with voltages that can have transient spikes as high as 3.0kV but my DVM only measures up to 1kV and 97% of the time I am under this range. I bought this and it was perfect the only problem is that it has a...
  19. Kloud

    Minimum horizontal force needed so book does not fall?

    Homework Statement Part C of problem Please see attachment : What is the minimum horizontal force needed to keep the book from slipping. Note that P=515N, and P=normal force, Fs=131.32N, Us=.255, M=9.85kg Homework Equations Fn=(m*g)/Us The Attempt at a Solution My answer is 378.549N, which...
  20. M

    I Calculating semi-major axis and minimum mass of an exoplanet

    Hello guys, I'm doing my physics coursework on kepler's third law and I'm finding the minimum mass and semi-major axis of a unknown planet. I have the following data: Stellar mass Mstar = 1.31 ± 0.05 Msun Orbital period P = 2.243752 ± 0.00005 days Radial velocity semi-amplitude: V = 993.0 ±...
  21. K

    Complete Noise Analysis: to find the minimum detectable signal

    Problem Statement: my aim is to digitalize a 10ns narrow pulse coming from a photo diode with current ranging from 10nA-70mA, as its impossible to cover this dynamic range of >60dB using a single TIA i have an option of separating it to two channels as below using two diodes ofcourse Lowest...
  22. C

    What's the minimum initial speed to score

    Homework Statement Alex Morgan is going to kick a soccer ball into the Canadians goal during the 2015 world cup. Alex kicks the ball straight at the goal from 20.0 m away, and it launches off the ground at an 33.3 degree angle. Assume the goalie is busy faking an injury and ignore air...
  23. Dr. Octavious

    A Minimum Current for Fusion/Plasma

    Hello all, Say we ignore plasma instabilities and Lawson's criterion, what is the minimum current required (or how do I calculate it) to create fusion/plasma? For a deuterium-deuterium reaction, the potential barrier to overcome is 7.6*10^(-14) Joules and temperature T=3.6*10^9 K.
  24. I

    Is the minimum Gibbs free energy the same for every material?

    We were learning about the change in free energy in class, but I was wondering since the Gibbs free energy decreases as a system becomes more stable, is the minimum absolute free energy for a material the same for every material, or can other materials be more stable than others?
  25. entropy1

    B After the 'Theoretical minimum' series, what is essential to know about QM?

    The adagium of most quantumphysics-afficionado's is: "Shut up and calculate" - 'learn the formalism'. So I started with Leonard Susskind's 'Theoretical minimum' textbooks. So now I know a little (very little) about the formalism, I started to wonder to which extent I have to go to educate...
  26. R

    What is the minimum kinetic energy for this roller coaster ride?

    Homework Statement A rollercoaster has a loop with a radius of 12m. The coaster travels 50m and at point A, enters the loop. The average frictional force on the coaster is 40N. The mass of passenger is 50kg. What is the minimum kinetic energy required at point A to generate a velocity of 27m/s...
  27. S

    The principle of least Action proof of minimum

    Homework Statement Reading Feynman The Principle of Least Action out of The Feynman Lectures on Physics, Vol 2. Link to text http://www.feynmanlectures.caltech.edu/II_19.html So I'm having a problem proving that, section 19-2 5th paragraf, that "Now the mean square of something that deviates...
  28. srinaath

    What is the minimum number of poles in single phase motor

    three phase induction motor can have minimum two poles, so synchronous speed of the machine can be 3000rpm. While single phase motors have two windings - auxiliary and main winding, so minimum number of poles in single phase winding is 4??!...am i right?
  29. megisacat

    Finding Minimum Work to Compress Water

    Homework Statement Find the minimum work to compress 1 kg of water isothermally from p1=1 bar, T1=120C to a volume that is 1/3 the original volume. Homework Equations Energy balance Q-W=U+KE+PE The Attempt at a Solution So first I found the phase of the water (p<psat for that temp so...
  30. lep11

    Minimum of piecewise defined function

    Homework Statement [/B] Let ##f:ℝ→ℝ## such that ##f(x)= \left\{ \begin{array}{l} 2x^4+x^4sin(\frac{1}{x}), x≠0 \\ 0 , x=0 \\ \end{array} \right. ## a.) Prove ##f## is continuous and differentiable everywhere. Find the (global) minimum (##f(x_0)##) of ##f## and point ##x_0##. b.)...
  31. M

    MHB Galois Groups and Minimum Polynomial

    Question This is what I have done so far. I was wondering if anyone could verify that I found the correct minimum polynomial and roots? If I am incorrect, could someone please help me by explaining how I would find the min polynomial and roots? Thank you.
  32. D

    Find the minimum kinetic energy of two electrons in a 1D box

    Homework Statement Problem: Consider a "crystal" consisting of two nuclei and two electrons arranged like this: q1 q2 q1 q2 with a distance d betweem each. (q1=e, q2=-e) a) Find the potential energy as a function of d. b) Assuming the electrons to be restricted to a one-dimensional...
  33. E

    A Information contained in minimum value of truncated distribution

    Suppose that a given population is endowed with a pair of characteristics T and K. Let's think of these characteristics as random variables (T,K)∼BiNormal((μT,μS),(σT,σS),ρ) I observe the realisations of T for a sample consisting of those individuals with K<a, where the selection threshold a...
  34. R

    Secant Method Minimum Estimation

    Homework Statement I am having some trouble understanding the following solved problem: Use two iterations of the Secant method to estimate where ##x^2 -x## has a local minimum. Start with ##x^{(0)} =1##, ##x^{(1)} =1/2.## Answer: Homework Equations Secant iteration: $$x_k = x_{k-1} -...
  35. anemone

    MHB Find Min of $\frac{a(x^2+y^2+z^2)+9xyz}{xy+yz+zx}$ for $x+y+z=1$

    Find, in terms of $a$, where $a \gt 0$, the minimum value of the expression \frac{a(x^2+y^2+z^2)+9xyz}{xy+yz+zx} for all non-negative real $x,\,y$ and $z$ such that $x+y+z=1$.
  36. blueray101

    The minimum applied force before an object slips off wall

    Homework Statement A horizontal force F is applied to hold a block, mass m = 1.7 kg against a vertical wall. The coefficients of kinetic and static friction between the block and wall are 0.81 and 0.87 respectively. F is gradually reduced until the block falls. Just before it falls, what is the...
  37. 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...
  38. ivtec259

    Quarter mile 10s car minimum power requirement

    Hi everybody! I am facing a problem in calculating the theoretical minimum power requirement P of accelerating a mass m a distance x in a time t in a two-stage acceleration process. Stage 1: Constant force acceleration amax (maximum grip of the tires of a car limits acc.) Stage 2: Constant...
  39. Adraasa Kynuei

    B What would be the minimum size for a galaxy to have a disk form?

    So looking at pictures of dwarf galaxies and how they're just an irregular (pun intended) mess and they do not have the disk shape that we, ironically, associate with galaxies despite a small minority of galaxies being big enough to have and maintain their disk shape. Like apparently the...
  40. anemone

    MHB Find Min of $(a-1)^4+(b+2)^4$ w/ $a+b\ge 3$

    Let $a$ and $b$ be real numbers such that $a+b\ge 3$. What is the minimum value of the expression $(a-1)^4+(b+2)^4$?
  41. N

    Optimizing Forces in Towing: Minimizing FB for a Given Resultant Force

    Homework Statement The truck is to be towed using two ropes. If the resultant force is to be 950 N, directed along the positive x axis, determine the magnitudes of forces FA and FB acting on each rope and the angle q of FB so that the magnitude of FB is a minimum. FA acts at 20° from the x-axis...
  42. A

    What is the minimum number of Polarizers needed

    Homework Statement A polarized light is incident on several polarizing disks whose planes are parallel and centred on common axis. Suppose that the transmission axis of the first polarizer is rotated 25° relative to the axis of polarization of the incident light, and that the transmission axis...
  43. E

    Minimum energy needed for a positrons to tunnel

    Homework Statement 10^12 positrons of the same kinetic energy are incident on 10eV, 1nm barrier. What is the minimum kinetic energy the positrons need before any of them can penetrate the barrier? Homework Equations p_T = e^(-2*a*L) a = (sqrt(2m(V_0-E))/hbar The Attempt at a Solution For...
  44. anemone

    MHB Prove the minimum is greater than or equal to 8

    Hello MHB! I've recently encountered the above really hard and good inequality problem that I failed to prove, I've been trying it for days but ALL my attempts proved futile.:mad: I feel completely defeated, and hope to get some useful hints to solve it from MHB... Thanks in advance for...
  45. J

    Dynamics: minimum velocity to prevent slipping

    Homework Statement A 200 lb man lies against the cushion on a Rotor ride, which is inclined at θ=10°. The coefficient of static friction is μs=0.3. Radius is 8 ft. Find minimum speed so that the man does not slip down. Homework Equations ΣFn = man ΣFz = 0 an = v2/r The Attempt at a Solution...
  46. F

    Find absolute minimum of f(x)=sin(x)-cos(x) on [0,pi]

    Homework Statement Find the absolute minimum of f(x)=sin(x)-cos(x) on [0,pi] Homework Equations - The Attempt at a Solution I know the answer is 0 from looking at a graph, but I cannot figure out how to express my workings algebraically. The end goal of this is to do a presentation on how I...
  47. A

    Minimum wavelength of electrons ejected from metal

    Homework Statement This problem has two parts. A laser produces photons having an energy, E = 3.5eV. a) What is the wavelength of photons produced, assuming that the index of refraction is 1.6? ->221nm b) If this laser beam is focused on the clean surface of a metal having a work function of...
  48. heartshapedbox

    Minimum force to make box slide down slope

    Homework Statement If m=5.0kg, φ=30◦ and μs =0.87, what is the minimum force needed to make the box slide down the slope? [/B] Homework Equations force of status friction is less than or equal to the normal force multiplied by the coefficient of static friction F,normal=mgcosφ The image...
  49. A

    Minimum Period of Oscillation Disk

    Homework Statement how far from the rim of a disk of Radius R must the pivot point be located in order for its period of oscillation to be a minmum where R is the distance from the point to the centre of mass? I'm stuck at the derivative because I saw a similar problem where the answer is...
  50. anemone

    MHB Find Minimum of $(a+b)(b+c)$ | Proof Provided

    Find, with proof, the minimum value of $(a+b)(b+c)$ where $a,\,b$ and $c$ are positive real numbers satisfying the condition $abc(a+b+c)=1$.
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