find the formula for a cubic polynomil ax3+bx2+cx+d with a critical point at x = 2 , an inflection point at (1,7) and a leading coefficient of 1

Q: Find the global maximum and minimum values of f(x, y) = 2x3 +y? – 24x on the Q2. closed region D =…

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Q: Use lagrange multiplier to find dimensions (X, y) of rectangular with maximum area and having a…

A: Given:  Circumference of rectangle is 144 Let X, Y denotes the length and breadth of a rectangle…

Q: 1. Find the orthogonal trajectories of the given family of curves: a. y = Ce-mx; with m held fixed

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Q: 1. Find where f(x, y) = 4x² + 8y? – 4x – 8y +5 has absolute extreme values over the square with…

A: To calculate the extreme values of f(x,y)bounded by the square, the following calculations need to…

Q: Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that…

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Q: li'm, n are positive integers and the equations x² + mx + 2n = 0 and x² + nx + m = 0 have real rots.…

A: According to question, Given quadratic equation,x2 + mx +2n =0,andx2 + nx +  m = 0,above  quadratic…

Q: Find the minimal solution of x+2y-z = 1; 2x+3y+z = 2; 4x+7y-z = 4.

A: Given:

Q: Use the method of Lagrange multipliers to find three positive real numbers, x, y, and z whose…

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Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

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Q: Use Picard's theorem, find the largest interval for which the IVP (x – 8)(x – 1) -y'%3D (x-6)(* +1)…

A: To find the largest interval on which existence and uniqueness guarantees a unique solution. For…

Q: Calculate E∫x3dx1dx2dx3, where E is the vertex tetrahedron (0, 0, 0), (1, 1, 0), (1, 0, 0),(1, 0,…

A: The solution is given as follows :

Q: Suppose the Earth is modelled by the unit sphere ²+y²+z² = 1 and the temperature at a given time is…

A: Given problem:Max: Tx,y,z=45x2+22y2-25z2subject to x2+y+z2=1 →  1Now   gx,y,z=x2+y2+z2-1=0Now…

Q: Use the Maximum Principle to solve the following dynamic optimization problem (1+ - u), z41 = 1; +…

A: We are given a dynamic optimization problem. And we have to find the optimal solution using Maximum…

Q: 1. Use agrange multipliers to find the extreme values of f(x,y)=2x²+ y on the circle x² + y² =1.

A: Here, f(x,y)=2x2+y and let g(x,y)=x2+y2, thus, the constraint is g(x, y)=1. So, fx(x, y)=4x; fy(x,…

Q: 7  please answer, type the solution if you can please. or write clearly

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Q: 1. An open top box is to be made from 48 m of wood with dimensions , y and z as shown in figure.…

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Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

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Q: Consider a circle of radius 2 centered at the origin. Use the Lagrange multiplier method to find the…

A: It is given that circle is of radius 2 and centered at origin. The function isfx,y=3x-y+5.

Q: 6. Find the extreme valucs of f(r,y) = ry subject to the constraint 4x2 + y? = 8 by using the method…

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Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x, y, z) =…

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Q: 7. Use the method of Lagrange multipliers to find the volume of the largest rectangular box in the…

A: Given question :- Find the maximum volume of rectangular box that can be inscribed in this ellipse.…

Q: By using the Lagrange multiplier, find the three positive number, x, y, and z whose sum is h and…

A: Here, you have to maximize the function x4y8z7, subject to the condition that x+y+z=h⋯⋯1. In order…

Q: Use simplexmethod to solve the given LPP Maximize z = 6xi+8X2 subject to, 3oxi+20r2<300 52+lox25 llo…

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Q: Q1: Use ewton- Raphson method to estimate the Yoot of fcx) = x -x -1 , emp loying an initial %3D…

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Q: 2. Find the absolute maximum and minimum values of f(x, y) = 4x+6y-(r²+y?) on the rectangular region…

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Q: Find the minimum value of f(x,y)=x^2+y^2 subject to the constraint 6x+4y=18 using the method of…

A: Given f(x,y)=x2+y2g(x,y)=6x+4y−18

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

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Q: 2. Find the least quadratic fit of the form y = ax² + bx +c for the data. Set up by hand. Solve…

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Q: find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the…

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Q: Construct a suitable Lyapunov function of the form ax? + cy², where a and c are to be determined,…

A: Since you have asked multiple question, according to our guidelines we will solve the first question…

Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: O Sobve the eava tíon X-6 上3 X-4 2x-1 243 4 Kt6 3. 2X-3 V-3 X-3 3D0 X+A 4 Xt6 -3 X-h 3.

A: This question can be solved using properties of determinant.

Q: 9) **Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: The given problem is to find the highest and lowest temperatures for the given temparature equation…

Q: 8. (a) Use the Lagrange multiplier method to find the minimum value of among all positive x, y…

A: we need to use langrange multiplier method

Q: Use the method of Lagrange multiplier to find the absolute maximum and absolute minimum values of…

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Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x,y, z) = 2x²…

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Q: Use Lagrange multiplier to solve. Max U = x+y+z subject to xyz = 8

A: max U=x+y+z subject to xyz=8

Q: Find the family of orthogonal trajectories of the system of circles which pass through the origin…

A: To find  The family of orthogonal trajectories of the system of circles which passes through the…

Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

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Q: 5. Find the orthogonal trajectories of the family of hyperbolas x² - 2y = ax. %3D

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Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

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Q: simplex method

A: We have to solve the given problem by simplex method.

Q: For the family x² + 3y2 = c, find that member of the orthogonal trajectories which passes through…

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Q: 5  please answer, type the solution if you can please. or write clearly

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Q: 7. Use the method of Lagrange multipliers to find a relative minimum of f(x, y, z) = x2 + 4y? + 16z²…

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Q: B) Use Lagrange multipliers to find the dimensions of the closed circular cylinder of smallest…

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Q: 5. Define the terms : Skewness and Kurtosis.

A: In statistics there are two types of measures namely measures of central tendency and…

Q: Create a 2nd order, homogeneous, linear IVP, that is not guaranteed to have a unique solution at…

A: Let's a take a 2nd order, homogeneous, linear IVP. For second order differential has a unique…