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. greg_rack

    Maximum tension in a cable holding a drawbridge

    My result for this problem is correct, but I would like to submit to you the method I used since it doesn't convince me. The problem asks for the maximum tension on the cable from the transition to 0 to 90 degrees; I firstly concluded just by thinking, not using formulas or particularly formal...
  2. FEAnalyst

    Maximum shear stress in an assymetric cross-section

    Hi, the formula for average shear stress in cross-section due to bending is simple: $$\tau=\frac{V}{A}$$ There’s also a formula for maximum shear stress in cross-section: $$\tau_{max}=\frac{VQ}{Ib}$$ But, from what I know, this equation is limited to symmetric cross-sections (rectangular, I...
  3. Andrei0408

    Inclination angle of a banked turn in a road for a maximum speed

    I know the solution is based on velocity and the sliding friction coefficient, and I believe I should put the condition Fcf smaller than Ff, but I just don't understand how to include μ in the solution, to find the angle. Even if you don't solve the problem, I just need to understand the...
  4. anemone

    MHB Find maximum area of a triangle

    Given two moving points $A(x_1,\,y_1)$ and $B(x_2,\,y_2)$ on parabola curve $y^2=6x$ with $x_1+x_2=4$ and $x_1\ne x_2$ and the perpendicular bisector of segment $AB$ intersects $x$-axis at point $C$. Find the maximum area of $\triangle ABC$.
  5. Hamiltonian

    Maximum extension in a system with two blocks separated by a spring

    the acceleration of the center of mass is ##a_{cm} = F/(M+m)## I considered the forces on the block of mass m(when the system is at maximum extension) I got the equation $$kx - \frac {mF}{(M+m)} = ma_{cm}$$ and from that I got the value of the maximum extension $$x = \frac {2mF} {k(M+m)}$$ which...
  6. P

    Position for maximum electric field between two wires

    For the first part, since $$ E(r) \propto \frac{1}{r} \hat{r}$$ by the principle of superposition the maximal electric field should be halfway in between the two wires. Then I'm not sure how to go about the second part of the question. I understand that the total potential due to the two wires...
  7. anemone

    MHB Max Value of |bc| for Complex Numbers in Inequality

    $a,\,b,\,c$ are the complex numbers in $|az^2+bz+c| \le 1$ for any complex number $z$ where $|z| \le 1$. Find the maximum value of $|bc|$.
  8. L

    Maximum velocity of an electron emitted from lanthanum

    Mass of an electron = 9.1*10^-31 Well, to find the maximum kinetic energy of the electron use E=hf, E=hc/λ=6.63*10^-34*3*10^8/1.5 *10^-7 E=1.326 *10^-18 J 1/2m v^2 max=E Rearrange in terms of v: v=√2E/m v=√2*1.326 *10^-18/ *9.1*10^-31 v=1707127... ~ 171000 ms^-1 Where have I gone wrong here?
  9. person123

    I Maximum Strain For Samples of Different Cross-Sectional Areas

    I would assume that because the samples are made of the same material they would fail at the same stress and so the same strain. However, the data shows that the sample with a greater cross-sectional area fails at a greater strain, and the two are roughly proportional. Does anyone know what...
  10. archaic

    Maximum electric field at the surface of a Van de Graaff generator

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  11. anemone

    MHB Maximum and minimum of a function

    Let $a$ be an integer. Consider the function $y=\dfrac{12x^2-12ax}{x^2+36}$. For what integral values of $a$ the maximum and the minimum of the function $y=f(x)$ are integers?
  12. jaychay

    MHB Determine the relative maximum and minimum on the graph

    Given that f is the function on (−∞, ∞) and the graph is the derivative of f 1.) Find the critical point on the graph ? 2.) Find the interval of the increasing function on the graph ? 3.) Find the interval of the decreasing function on the graph ? 4.) Find the point which is the absolute...
  13. S

    Formula for maximum interference for reflected light (thin - film)

    The light comes from glass to boundary of glass and soap film, then there will be light which is reflected and transmitted. The reflected light has no phase shift and the transmitted light will hit the boundary of soap film and vacuum and the reflected light from this boundary will also has no...
  14. jisbon

    Engineering Computing the Maximum Power delivered to a Resistor

    Hi all, Checking my answers here as it doesn't seem to match with the answers given to me. Would appreciate if anyone could point out the mistakes I made. First I will compute Rth. Offing all independent sources, applying a known voltage across R (in this case 1v) and using mesh analysis...
  15. B

    Spring-mass system in circular motion has a maximum angular speed?

    and this is my solution for question (d), it may seems that $$R=(k)/(k-m\omega^2)R_0$$ so that $$\omega ≠ \omega_i =√(k/m)$$ but $$\omega_c <\sqrt{k/m}$$ is always true, ##\omega_i## corresponds to the limit case when ##F_max## is infinitely large Besides, I don't know other Physics prevents...
  16. R

    When is the rate of change of Kinetic Energy maximum here?

    Because, ##F=ma=kv##, therefore, ##a=kv/m##. Clearly, the net acceleration ##A=-(g+a)##. Also, ##A=dv/dt=-(g+ \frac {kv} m )##, so cross multiplying and integrating LHS with respect to ##v## and RHS with respect to ##t## gives me: $$ v= e^{ \frac {-tk} m } * (u + \frac {gm} k) - \frac {gm} k $$...
  17. Frigus

    Why the current is maximum When Rᵉˣᵗᵉʳⁿᵃˡ=Rᴵⁿᵗᵉʳⁿᵃˡ?

    My teacher proved it like this I= ##\frac {E}{R+r}## Where R is external resistance And r is internal resistance E is emf of the cell, Now we can write it like this I= ##\frac {E}{(√R-√r)²+2√R√r}## if R=r then the denominator value will be minimum but i am unable to understand that why this is...
  18. R

    Variable friction on an inclined plane and maximum velocity

    This problem was from the chapter on Work and Energy so, I thought of using the principle of conservation of mechanical energy. Clearly, the potential energy of the block decreases by mgh (assuming the block has mass m). This energy should have been converted to kinetic energy, but it clearly...
  19. tworitdash

    A Maximum reception/transmission criteria for Conical Horn Antennas

    I have written a solver for my thesis which determines various parameters of a conical horn antenna for astronomy application. It is done with Mode Matching Technique (MMT) and some Rumsey's integrals for the aperture free space transitions. I have made some goal functions with the solver which...
  20. ItsukaKitto

    Maximum height a block reaches after separating from a curved moving ramp

    Diagram attached at the endI personally think there's something wrong with this question, and I'd like if someone can tell me whether it's the question that is wrong or my approach. If I attempt the solution thinking that M should be stationary, the solution is simple. 0 - 1/2 mv^2 = -mgh...
  21. Q

    Finding the maximum height of a projectile

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  22. jisbon

    Engineering Finding the maximum power delivered using Thevenin's theorem

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  23. P

    Calculate the maximum vertical point force P that this beam can sustain

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  24. J

    I Maximum violation of Bell's Inequalities?

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  25. N

    Mechanical engineering: Maximum Power Transmitted by a V-Belt Assembly

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  26. S

    Maximum possible speed of explosion fragments

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  27. Wrichik Basu

    What is the meaning of "Long time maximum output current ≥ 1.5 A"?

    I am looking at the module HLK-5M05, which is a ##5\ V, \ 5\ W## AC-DC power supply module. The advantage of this module is that, it does the stepping down and rectification within itself, and is a switching source, so fluctuations in the voltage grid won't affect the output (at least that's...
  28. J

    MHB Find the maximum amount of the equal annual withdrawal

    P25,000 is deposited in a savings account that pays 5% interest, compounded semi-annually. Equal annual withdrawals are to be made from the account, beginning one year from now and continuing forever. The maximum amount of the equal annual withdrawal is closest to A. P625 B. P1000 C. P1250 D. P1625
  29. dcheme7373

    Maximum mass of a black hole

    The question, "why didn't the emerging universe collapse into a black hole" has been answered in other forums. Though I am not sure I understand the reason. But it got me thinking. Is it particularly stupid to ponder whether a black hole has a maximum possible mass? Or rather a certain mass...
  30. T

    How to ensure maximum possible joint torque for an actuator?

    Below, I have a joint system that consists of a fixed anchor and a moving arm: What I want is simple: To attach a linear actuator on the moving arm in such a way that the mechanical advantage of the actuator is exactly 1 (Ie the actuator only has to generate exactly the amount of force as the...
  31. E

    The maximum length that a spring can stretch in reality

    In detail, I came up with 424m for the stretched length of a spring in order to change the mass of an object by 10^-9kg which originally was 1 kg. Problem said, "is it feasible?" In my opinion, there is no spring that can be stretched for this long, so it is not feasible. However, I'm not sure...
  32. W

    A PCA and Maximum Likelihood?

    Hi, I am looking into a text on PCA obtained through path diagrams ( a diagram rep of the relationship between factors and the dependent and independent variables) and correlation matrices . There is a "reverse" exercise in which we are given a correlation matrix there is mention of the use of...
  33. caffeinemachine

    MHB Maximum value a function satisfying a differential equation can achieve.

    Let $f:\mathbb R\to \mathbb R$ be a twice-differentiable function such that $f(x)+f^{\prime\prime}(x)=-x|\sin(x)|f'(x)$ for $x\geq 0$. Assume that $f(0)=-3$ and $f'(0)=4$. Then what is the maximum value that $f$ achieves on the positive real line? a) 4 b) 3 c) 5 d) Maximum value does not exist...
  34. P

    What is the maximum depth to which a P-wave ray can travel?

    I've created an excel spreadsheet with the given model in addition to calculating radius of the layer by subtracting depth from 6371. I've calculated Zf. I've also found what I think is vs by doing alpha * (radius column/6371), but that could be wrong. I know I need to find where 20/6371 =...
  35. Sokolov

    Maximum voltage that can be applied to DC circuit with resistors

    I see that ##V_{ac}=V_{ab}+V_{bc}##, with ##V_{ab}=I_1R_1=I_2R_2## and ##V_{bc}=I_3R_3##. However, I don't see how to express mathematically the maximum value of ##V_{ac}##. Could someone please help me with this task?
  36. Ashish181

    Have You Calculated the Maximum Bending Moment Yet?

  37. E

    Maximum Distance a Projectile Moves Up an Inclined Plane

    the red line is the initial velocity, the grey parabola is the path of the projectile. hi there...I'm kinda stuck at the part b of this problem. I can do part a with no problem. can anybody explain to me how to do the differentiation needed to solve part b?? by explain I mean explain the...
  38. B

    Is 51 micro joules the maximum kinetic energy of this pendulum?

    So I have been given a question here which asks me to work out the maximum kinetic energy of the pendulum It has given info such as time period and amplitude, which I had then made use of these formulas Does a kinetic energy of approx 50.98 micro joules seem right here? Any help would be...
  39. J

    Proper barograph linkage settings for maximum pen displacement?

    Hi. I wasn't sure where to post this. It does relate to Earth science, but still wasn't sure whether or not to post there. Anyway, I am trying to determine the proper settings of the linkage of my barograph so that the pen moves the greatest distance up or down on the chart with as minimal...
  40. E

    Minimum frequency for a point to have maximum amplitude in standing wave

    When I tried using the equations the only thing I could see is that it is impossible for such point to be an anti-node. In this case, how do I find the frequency? The answer is not even with the form of v*n/2L which is very confusing to me, I thought that the frequency of a standing wave must...
  41. C

    Ideal Ball weight to get the maximum range from a ball launcher?

    Hello guys, i am building a ball launcher to proper a line of baits into the sea, the line has 25 baits, each bait weights 30 grams (about 1oz) ideal shooting degree seems to be 45 to get maximum range, What I would like to figure out is the ideal weight of the ball to achieve the greatest...
  42. J

    Maximum mechanical actuator strength allowed by physics

    What is the strongest actuator (that can exert a controlled amount of force & be able to start/stop linearly or rotationally) that an infinitely advanced civilization could create, and how (what object/process) would they do it? It must be non-lethal or be shielded to be non-lethal at a distance...
  43. R

    Maximum Acceleration: I Got the Correct Answer

    I got the correct answer which is √g. I solved it as if it were a circular motion with radius of 1. But got no idea why my solution did work.
  44. neilparker62

    I How Does Elastic Collision Angle Relate to Mass Ratios?

    Large mass (M) - moving - collides elastically with stationary small mass (m) as per crude diagram below. Angle θ is formed between the initial path of the large mass and the line of centres during collision. I would like to say that maximum deflection of the large mass occurs when cos(θ)=m/M so...
  45. WMDhamnekar

    MHB Maximum area of rectangle which circumscribes the given quadrilateral.

    Suppose, a rectangle circumscribes a quadrilateral having length of diagonals p and q, and area A.What is the maximum area of rectangle that circumscribes the given quadrilateral? Answer:- How to answer this question using geometry or calculus or by using both techniques.
  46. bravopipo

    Maximum load capacity of a time dependant Force on the surface of a metal

    Hello; What equations on mechanics can I use or study in order to measure the maximum force in Newtons the surface of the metal Steel box can hold. Details: Watch the image below, we have a metal box made of let's say steel, this box have a shape of rectangle of a thickness of for example 1cm...
  47. E

    Maximum compression of a spring?

    I found the amplitude of the simple harmonic motion that results (0.367, and I know this is correct because I entered it and it was marked as a correct answer), and assumed it would be the same value for the maximum compression since x(t) = Acos(wt). And, since the maximum value of cosine is 1...
  48. B

    Solving Math Problem with Crates: A Maximum Dividers Challenge

    Hello everyone, I hope I'm not intruding with too simple of a request for help. I have this math problem: A rack space with 100 slots for plastic crates. I have two type of crates, one with 20 dividers weighing 5 grams and one with 60 dividers weighing 25 grams. I want to add crates to...
  49. Arman777

    I Calculating the Maximum total neutrino mass by using cosmological boun

    In an article its written, $$\Omega_{\nu} = \frac{\rho_{\nu}}{\rho_{crit}}=\frac{\sum m_{i,\nu}n_{i,\nu}}{\rho_{crit}} = \frac{\sum m_{\nu}}{93.14h^2eV}$$ Now I am trying to derive this for myself but I could not. Can someone help me ? So the values are, ##\rho_{crit} = 1.053 75 \times...
  50. S

    Maximum compression of spring

    1/2 m v2 + mgh = 1/2 k x2 1/2 (5) (9) + (5) (9.81) x = 1/2 (200) x2 100 x2 - 49.05 x - 22.5 = 0 x = 0.779 m or x = - 0.289 m Answer key says the answer is 0.289 m but in my opinion the answer should be 0.799 m because I take h = 0 at the position where the spring has maximum compression so...
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