# What is Minimum: 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. ### I Gradient descent algorithm and optimizers

Hello, To find the minimum (global or local) of a function, we can set the function's gradient equal to zero and solve for the $x$. This is the classic, analytic approach to find the minimum and it works if the function is differentiable and if it has not to many parameters (how many?) An...
2. ### Show that the minimum in alpha-decay spectrum is caused by interference of peak

This problem set considers (beta-delayed) alpha decay of ##{}^{20}Na##. I'm currently stuck in the following exercise and was hoping some of you could help me in the right way. Thanks in advance! The problem is: c) The experimental spectrum of ##{}^{20}Na## can be found below. Apart from peaks...
3. ### Engineering Minimum Hamming Distance for Parity Check Matrix

My answer: Then, if I am not mistaken, the solution made in that video is mostly guessing about which columns combination can be equals to zero and I found 1st, 2nd, and 3rd rows as well as 2nd, 3rd, 4th rows are equals to zero so the minimum hamming distance is 3 since my answer is mostly...

5. ### Where in orbit should a rocket fire to escape with minimum ΔV

I am really lost on how to deal with this. Since this is an elliptic orbit, the mechanical energy is negative. For the rocket to escape orbit, we have to get the mechanical energy to be equal to or greater than zero. I thought at first that it would escape in the perigee, since that's where the...
6. ### I Checking if a stationary point is a minimum using Lagrangian Mechanics

I'm having trouble understanding how to find out whether or not a stationary point is a minimum and I'm hoping for some clarification. In my class, we were shown that, using Euler's equation, the straight-line path: with constants a and b results in a stationary point of the integral: A...
7. ### I Why is the minimum energy equal to the energy uncertainty?

I was watching this video on Youtube, however, I don't get the step at 14:50 where he says that ΔE≥½hf means that E0=½hf. Could someone explain why the minimum energy is equal to the energy uncertainty?
8. ### I Minimum light bulb wattage for solar simulator

I am trying to design a simple homemade PV solar simulator. I have picked metal-halide lamps as my light source. If the PV panel has an area of 1m^2 and I wanted to achieve spatial uniformity across the irradiated surface with an irradiance of 1000 W/m^2, how do I go about selecting what...
9. ### Calculate the minimum force required

I tried taking the components but got stuck there on what value of theta I should take
10. ### Evaluating minimum and maximum values with calculations

Hi! I know this may seem like a silly question but I really just want to make sure I understand this correctly. I've already calculated the minimum and maximum values for time and height: t min = 0.58 s t max = 0.68 s y min = 1.98 m y max = 2.02 m To calculate the minimum average speed, would...
11. ### How to find minimum possible mass

Unfortunately, this is not the right answer.
12. ### Minimum screw thread engagement to support weight?

Hello All, I know there are rules of thumb and thread engagement calculators online but I am trying to find mathematically what the minimum number of threads acceptable would be. I currently have an eyebolt that will be torqued to a specific value. This eyebolt setup will then need to lift a...
13. ### Minimum Length of Cuts for Unfolding Box Into Flat Sheet?

Hi everyone I got 36 cm as the answer for the following problem, but it's supposed to be 32cm. These are the cuts I have 4 x 5cm = 20cm 2 x 3cm = 6 cm 1 x 10cm = 10cm which adds up to 36cm. I can get 32cm with 4x3=12 2x5=10 1x10=10 But I don't think that would be the correct net. Is...
14. ### I The Theoretical Minimum: Length Contraction and Time Dilation

Hello, My name is Dave and I'm a physics major at UIUC. It looks like I will be taking the special relativity course (phys 225) this fall. I've always been fascinated by the theory so I decided to get a head start with Lenny and Art's perspective on it. My first head-scratching moment came in...
15. ### I Request for an example of minimum energy principle (thermodynamics)

Summary: Request for an example of minimum energy principle usage The minimum energy principle states that, for a system at constant entropy, volume and other extensive quantities, the internal energy is minimized at equilibrium. Can you give me an example in which, using this principle, is it...
16. ### MHB Minimum of product of 2 functions

Hello Simple question Whether the minimum of the product of two functions in one single variable, is it greater or less than the product of their minimum thanks Sarrah
17. ### I Postulating a minimum gravitational field strength

this paper postulating a minimum gravitational field strength postulating a minimum gravitational field strength (minimum curvature) and a minimum acceleration but otherwise leaving Gr could reproduce MOND [Submitted on 25 May 2022] MONG: An extension to galaxy...

33. ### MHB Which procedure takes the minimum time to solve modulus functions?

1) -|2x-3|+|5-x|+|x-10|=|3-x| 2) |2x-3|-|5-x|-|x-10|-|3-x|=28 3) -|2x-3|+|5-x|+|x-10|≥|3-x| How can we solve these problems? The method I know is to plug in the critical values to see which modulus becomes positive and which one becomes negative. Then find out the values of x for which the...
34. ### Medical Minimum amount of sleep per night for 4 months

I am a 17 year old male with no major health conditions. I want to know if there will be any long term effects of less sleep(and practically no sleep schedule) ranging from anywhere between 4-5 hours a night(sprinkled with occasional all-nighters) for a period of 4-5 months. a quick google...
35. ### Minimum Tone Spacing: Coherent Frequency Shift Keying

Hi, I was reading through some online notes and was wondering: when dealing with coherent FSK, what is the minimum tone spacing and why? I know that for non-coherent FSK, we can show that the minimum is: ## f_1 - f_0 = \frac{1}{T} ## where ## T ## is the symbol period. However, if we are now...
36. ### Minimum motor power for a mechanical horizontal sieving machine

r = 2.5 l=10 cm angle = 0 (maximum connecting rode elongation) w = 0.5 (30 rpm) n=10/2.5 = 4 so the acceleration is 1.5×0.5×0.5(1 + 1/4 ) = 0.4 m/s friction force = 10*9.81*0.3 = 29.4 Newton. Crank force is the mass of the object into acceleration. So crank force = 10 × 0.4 = 4 Newton...
37. ### MHB Prove the minimum and maximum edges in a graph

Hello! I am having trouble solving the right part of the inequality. For left part of the inequality $n-k \le m$, here’s how I did it Let $n = v_{1} + v_{2} + v_{3}...+v_{k}$, the sum of vertices of each component in G least number of edges = $(v_{1}-1) + (v_{2}-1) + (v_{3}-1)...+(v_{k}-1)$...
38. ### RF Transistors, is there a 'minimum' frequency where they work?

Some RF transistors are not 'characterised' for lower frequencies, can they still be used? I get that a lower operating frequency (HF/1.8MHz) may not be the commercial target for an UHF transistor (>136MHz) so no effort spent on characterising them. Likewise HF transistors >1.8MHz not...
39. ### Minimum length x for no slipping

I'm letting the weight of the hanger be W. Since there is no slipping, the total frictional force will be = total weight. When the load of 50W is placed at X, there'll be a normal force at the left end of the pole on top to the left, and another normal force at the right end of the pole at the...
40. ### MHB Finding the Minimum $x$ for a Prime Product

Find the minimum value for $x$ where $x\in \mathbb{N}$ and $x^2-x+11$ can be written as a product of 4 primes, which are not necessarily distinct.
41. ### Minimum voltage supplied to motor windings

I have seen the following specifications in the Hurst motor data sheet. i have confusion on the Minimum DC voltage to the motor windings. It says as 10Vdc, but even if i give less than 10V it should not damage the motor windings. I can understand the upper voltage if i cross it may damage the...
42. ### Using an ODE to show a local minimum

The ODE given to us is y' = xcosy. I am having a bit of trouble when it comes to solving this problem. We are supposed to show that the solution has a local minimum at x = 0 with the hint to think of the first derivative test. However, I am only really familiar with the first derivative test...
43. ### Minimum energy of a photon to produce ##\pi^+##

I have a doubt about the first request: I suppose to find the minimum energy of ##\gamma## in the situation where ##p## is stationary, there is no reason to say that the proton is stationary if I were to calculate it in the CM, right?. So I have to consider che LAB-frame to find ##E_\gamma##...
44. ### Minimum or Maximum value of a multivariate function

First thank you for taking your time to take a look at this simple question. And sorry for the informal math language and equations, I hope you guys can understand it. So, depending on the case, I have 2 or 8 simple quadratic functions f(a), f(b), f(c),… f(z). Each a,b,c,…,z have a different...
45. ### What is the minimum gyroscope speed to yield force precession?

Does anyone know what the minimum speed of a gyro to make it so a force at 0deg will yield a movement at 90deg... or even better, what the angle is wrt speed... see http://www.copters.com/aero/gyro.html for pictures. -thx, rich
46. ### MHB Find path to minimum cost from start to finish

Hey! 😊 I am looking the following: The board of a game is an $M \times N$ board with squares, where the starting point is on left - in position $(0, 0)$ - and the finish is in the lower right - in position $(M-1, N-1)$. Each square contains a positive number that describes the cost of moving...
47. ### MHB [ASK] Minimum Surface Area

The volume of a cuboid box with a square base is 2 litres. The production cost per unit of its top and its bottom is twice the production cost per unit of its lateral sides. Suppose the side length of its base is x and the height of the cuboid is h. The minimum production cost is reached when...
48. ### MHB [ASK] Minimum Length of AP + PB

The point A is located on the coordinate (0, 5) and B is located on (10, 0). Point P(x, 0) is located on the line segment OB with O(0, 0). The coordinate of P so that the length AP + PB minimum is ... A. (3, 0) B. (3 1/4, 0) C. (3 3/4, 0) D. (4 1/2, 0) E. (5, 0) What I did: f(x) = AP + PB...
49. ### MHB Min Value of $a^2+b^2$ in Quadratic Equation

Determine the minimum value of $a^2+b^2$ when $(a,\,b)$ traverses all the pairs of real numbers for which the equation $x^4+ax^3+bx^2+ax+1=0$ has at least one real root.
50. ### MHB Minimum Length of Longest Side in Inscribed Triangle

In triangle ABC, ∠C = 90 degrees, ∠A = 30 degrees and BC = 1. Find the minimum length of the longest side of a triangle inscribed in triangle ABC (that is, one such that each side of ABC contains a different vertex of the triangle).