Minima Definition and 110 Threads

My first post and I am new to forum etiquette, please go easy on me. I have an exam in a few days and have a good grasp on the content. Historically the professor has been putting harder Lagrange questions on the exam than are available in my textbook and supplement books or that I can find...

Homework Statement A corridor of with a is at right angles to a second corridor of width b. A long, thin, heavy rod is to be pushed along the floor from the first corridor into the second. What is the length of the longest rod that can get around the corner? Homework Equations I...

I've been working on a decentralized algorithm for finding local minima. Can anyone give me a few examples of mappings of the form F:R→R that have multiple local minima. I'm having problems defining neighbourhood on mappings from R2→R, so I thought I'll test it out on single variable functions...

Homework Statement Locate all relative maxima, relative minima ,and saddle points if any. f(x,y)=ysinx fx(x,y)=ycosx fy(x,y)=sinx ycosx=0 sinx=0 y=0 x=0,∏,2∏... up until infinity Critical points at (0,0),(∏,0),(2∏,0)... fxx(x,y)=-ysinx...

Homework Statement Consider the following function of the variable r, r>/=0 y(r)=(r^(2)-5.50r)exp(-r) Find the value of the first derivative dy/dr at r=5.50 Homework Equations How do I solve this? I know its a simple derivative equation, but I can't seem to get it. I tried finding the...

The cycloid is defined by the parametric equations x = a(t-sin(t)) and y = a(1-cos(t)) I am trying to find the set of points of relative extrema of a cycloid. I differentiated first to get \frac{dx}{dt} = a(1-cos(t)) and \frac{dy}{dt} = a*sin(t) Then, by the chain rule...

Here's the problem I'm trying to solve, We have an N dimensional surface. We do not know the form of this surface however we have datapoints which are likely to be close, though not guaranteed to be on the surface, with some outliers. What I want to do is determine where in N dimensional...

Homework Statement Consider the function f(x) = sin (x) in the interval x ∈ (p/4, 7p/4). The number and location(s) of the local minima of this function are? Homework Equations The Attempt at a Solution I have managed to get one of the minimas (i.e. 3p/2), however i am unsure about...

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle. is this way correct? assume that x is side of square and r is radius of circle k=4x+2∏r sum of...

Homework Statement http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Physics%20%289702%29/9702_s09_qp_2.pdf number 5b The speed of sound is 330ms-1 The frequency of sound from S1 and S2 is increased. Determine the number of minima that will be...

Could you pls advise me any reference (textbook for example) where I can find how to calculate maxima minima of function of several variables... or drop a couple of lines here.. Thank you

Homework Statement I am given the problem "A function is defined by f(x) = 1-x^(2/3). a. find the minima and maxima of the function. State whether they are relative or absolute. b. graph the function." Homework Equations I found the derivative and set it equal to zero. y' =...

Homework Statement F(x)=(x^2)/(x+1) Find critical points Find local maxima & minima Homework Equations None The Attempt at a Solution F'(x) = x(x+2)/(x+1)^2 crit points: -2,0,-1 f(-2) = -4 f(0) = 0 f(-1)=undef My book is telling me that f(0) is the minima, and f(-2) is the...

Homework Statement ## f\left( x,y\right) =x^{2}-4xy+6x-8y+2y^{2}+10 ## ## f_{x}=2x-4y+6=0 ## ## f_{y}=-4x-8+4y=0 ## ## f_{y}=-4\left( x-y+2\right) ## -2=x-y, then solving fx and using this equality ## f_{x}=0=2\left( x-2y+3\right) =0 ## 2(-2 -y+3)=0 2(1-y)=0 y=1, then pluggin...

1.Find the vertical and horizontal asymptotes (if any), intervals of increase and decrease, local maximum and minimum values, intervals of concavity and inflection points for f(x) = 1 / (L - x^1/2) 3. I found the vertical asymptote to be "x=0" , I found the horizontal asymptote to be "y=0" So...

Homework Statement This is question is from my test paper. Find the minimum value of 9tan2x+4cot2x. I wasn't able to solve it during my examination. But later i remembered that i can find its minima which unfortunately my teacher still hasn't taught. :( I have a very little knowledge of it so...

Please teach me this: Why the minima of potential of classical Lagrangian is called the ''vacuum expectation value of Phi(field function)''.Is it really a vacuum expectation value of field operator at the vacuum states(at this state,the potential part of classical Lagrangian equals zero)...

Homework Statement minimiza f(x) = x_1 subject to (x-1)^2+y^2=1 (x+1)^2+y^2=1 Graph the feasible set, Are there any local minimizers and global minimizers? Homework Equations I have graphed the feasible set...

a problem in minima and maxima applicatios (urgent !)please Homework Statement A straight river 3km wide runs due east. A cable is to be laid from a point A on the south bank of the river to a point B on its north bank, 9km downstream from A. The cable is to be laid in a straight line from...

Hi there. I've got this function f(x,y)=(y-3x^2)(y-x^2), and I have to analyze what happens at (0,0) in terms of maxims and minims. But what I actually have to proof is that there's a saddle roof at that point. Theres is a critical point at (0,0). Let's see...

URGENT! michelson interferometer - maxima and minima Homework Statement If a wave is reflected at a surface of a plate with higher refractive index (eg. At air glass or air-metal) it suffers a λ/2 phase change. Show that for the interferometer, maxima will occur for 2dcosθ = (n+1/2)λ and...

Homework Statement Let An be the nth term of an A.P. and if A7 = 15, then the value of the c.d. that would make A3 x A7 x A12 greatest is : 1)9 2)9/4 3)3/8 4)18 Homework Equations The Attempt at a Solution Applying AM>=GM A3+A7+A12/3 >= (A3 x A7 x A12)^1/3 given that...

Homework Statement A farmer is planning to build six adjoining rectangular pens of equal size to house his hens, as shown in the diagram. He only has 180m of fencing, however, and he wants to make the pens as large as possible. Find the maximum area he could make each pen. The diagram is...

Homework Statement I do not have a specific homework problem, but could someone please clarify this for me? QUESTION: When you have an absolute maxima (or minima), how can you tell if it is ALSO a relative maxima (or minima)? I understand how to find absolute extrema on a closed...

What about the nonlinear forms of it? Or is it guaranteed to reach a global minimum?

Reading the derivation for the single slit diffraction minima formula from this site, I'm not convinced about its argument. http://www.math.ubc.ca/~cass/courses/m309-03a/m309-projects/krzak/index.html" What I'm having trouble understanding is the explanation of the formula for minima when m>1...

Hey my problem is that I am unable to calculate the absolute value of the following function: f(z)=\bar{z}(z-2)-2\Re z wherase z=x+iy What i did was: =|z|^2-2\bar{z}-2\Re z=x^2+y^2-2x+2iy-2x=x^2+y^2+2yi-4x and how should i calculate the absoulte value of this function?? Because i should...

Homework Statement What is the maximum slit width so that no visible light exhibits a diffraction minimum?(Visible light has wavelengths from 400 nm to 750 nm.) Homework Equations D*sin(theta)=m*lambda ; where D = slit width,theta in degrees, m =1,2,3,..., and lambda is wavelength...

Homework Statement Find the maximum and minimum values of f(x,y) = (xy)2 on the domain x2 + y2 < 2. Be sure to indicate which is which Homework Equations I am not sure what to put here. I solved this problem a different way, and I am not confident I did it correctly. The Attempt at a...

Homework Statement Determine the largest value of x_{1}^2 + x_{2}^2 + x_{3}^2 when x_{1}^2 + 2x_{2}^2 + 2x_{3}^2 + 2x_{1}x_{2} + 2x_{1}x_{3} + 2x_{2}x_{3} = 1Homework Equations Not sufficiently relevant to produce the expected answer.The Attempt at a Solution Completing the square, we get...

I am new, but i have a question about the TI -89 Titanium calculator, does anyone how if i can plug in the equation f(x)=2x^3-15x^2+36x-1 to identify each location of the local maximun and minimum, and inflexion poits? Will this calculator do this?

1. Find the absolute maxima and the absolute minima of the following function f(x)=(2x)/(x^2+1) on [-2,2]

Homework Statement What is the slit width? Wavelength is 635 nm. Distance between screen and slit, 2.5 m. Distance on screen between first and second minima above the central maxima is delta 6 mm. Homework Equations D* sin theta * = m * lambda tan theta = x/ distance between screen...

Homework Statement Please look at the attached picture In that I had to draw the line of maxima and minima Homework Equations line of maxima has greatest gradient line of minima has smallest gradient The Attempt at a Solution which line should be the maxima? the line with the...

Hi all, In my Calculus III course, we are using Stewart's book, so as you might know there is not much rigor in there. Likewise, when it came to the section on Maximum and Minimum values of a function with two variables z=f(x,y), they ommited a lot of stuff. Hence, i tried to use...

Homework Statement a and b are two perpendiculars drawn to the sides from a point on the hypotenuse of a right angled, isoceles triangle. Find the minimum value of the hypotenuse in terms of a and b. Homework Equations ABC is a right angled, isoceles triangle, with AC, the hypotenuse...

A rectangle is to be inscribed in a right triangle having sides 6 inches, 8 inches, and 10 inches. Determine the dimensions of the rectangle with greatest area. I recently tried doing it and the answer was found by finding the slope and then using the first and second derivatives of the area...

Are there any analytical techniques to do this besides the Derivative Test?

If the stationary points of a function are minimum points does that qualify the function to be a convex function? Also, if the function has only one stationary minimum point does that mean that that point is its global minimum? Can someone please confirm these for me Thank you

How will I find minima,maxima or both of one function (if they exist)? For example: f(x)=x^2-3x+2; f(x)=x^2-2x-x+2; f(x)=x(x-2)-(x-2); f(x)=(x-2)(x-1) x1,2=1,2 Those are the zeroes of the function. But how will I find the critical points (minima,maxima) of the function if x...

Homework Statement I did a physics lab the other day that dealt with two slit diffraction. In my setup, I also saw two faint diffraction minima, and it is my understanding that there is also some single slit diffraction effects. I measured the position a diffraction minimum to be y= 8.775...

for the equation... y = x^3 - 2x^2 -5x +2 is its local minima at (2.120,-8.061) Thanks

Homework Statement A)Two flat slides of glass are separated at one edge by a thin wire. The top surface of the upper slide and the bottom surface of the lower slide have special coatings on them so that they reflect no light. The system is illuminated with light of wavelength 418 nm. Looking...

Homework Statement For a monopolist's product, the demand equation is: p = 42 - 4q and the average-cost function is c = 2 + (80/q) Find the profit-maximizing price. Homework Equations When i started to solve the problem, i deduced...

Does the distance between the maxima increase/decrease or stay the same when the slit separation is increased? when the slit width is increased? what about if it was minima? thanks for any help to understand how this works.

I need to design a circuit to charge a capacitor with minima loss of dissipation through resistance. Any idea?

Homework Statement Problem goes like this: For a monopolist's product, the demand equation is: p=156-2q _ and the average-cost is c(ave)=120+112/q Homework Equations We need to find the total cost function in terms of c= The Attempt at a Solution...

Homework Statement A hypothetical star S has a planet P that moves in an elliptical orbit with period T . The minimum distance of P from S is d and the maximum distance is 1.7d. (i) find the maxima and minima of the magnitude of the acceleration of P, in terms of d and T . Homework...

Optimization, Minima, new question:Sheet Alluminum Homework Statement A box with a square base and no top must haave a volume of 10000 cm^3. If the smallest dimension in any direction is 5 cm, then determine the dimensions of the box that minimize the amount of material used. Homework...

I have a function that is not giving me critical points for where their appears to be a maximum. from plot their seems to be a cp at approximately x=y=5 However, these are the cp's: cpx = -0.2618 -1.3090 1.8326 2.8798 -2.8798 -1.8326 1.3090 0.2618cpy = -0.2618...