Show that the function f(x,y) = x³ + y³ – 63(x +y) + 12xy is maximum at (–7,–7) and minimum at (3,3).

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

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Q: Find the quadratic function f(x) = ax + bx +c that goes through (2,0) and has a local minimum at (0,…

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Q: Consider an arbitrary quadratic function f(x) = a.x² + bx +c where a, b, and c are constants with a…

A: We need to find second derivative test to check local maximum and minimum

Q: Find the maximum value and the minimum value of the function f(x, y, z) = x + y + z such that x2 +…

A: Given To find the maximum value and the minimum value of the function f(x, y, z) = x + y + z such…

Q: Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this…

A: Differentiate the function fx,y=5x-x3+2xy-y2 partially with respect to x and y, to obtain fx and fy.…

Q: Find absolute maximum and minimum values for f (x, y) = x² + 14xy + y, defined on the disc D = {(x,…

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Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: Consider the R² – R function f defined by f (1, y) = 2² – 6x +3y² - . (a) Find all the critical…

A: For critical points we need to find first order partial derivatives of given function and substitute…

Q: c) Find the second degree polynomial approximation to f at (a, b) = (1, – 2) T2(x, y)

A: Given :- The second degree polynomial approximation to f at a,b = 1,-2 f x,y = -x2y2x2 +y2

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Find the absolute maximum and minimum of f(x, y) = 3z +y within the domain z² +y? < 4.

A: Use lagrange multiplier.

Q: Find all points (x, y) on the graph of g(x) = 1/3 x3 - 3/2 x2 + 1 withtangent lines parallel to the…

A: Given: The function gx=x33-3x22+1, To find: All the points x,y on the graph of given function at…

Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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Q: The function f(x, y) = x3 + 3xy2-3x2 – 3y2 + 4 has a local maximum at (A) (0, 0) (B) (2, 0) (C) (1,…

A: Option (A) is correct.

Q: Determine the value of the Wronskian W(y1, y2) of y" - 2y + 1 = e2*(x + 1) if x-0.2 by using…

A: Given, y''-2y'+1=e2xx+1. The objective of the problem is to obtain the value of the Wronskian if…

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

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Q: Find the absolute maximum and minimum values of f(x, y)=x² +xy+y² -6y on D={(x, y)| -3<x<3, 0<y<5}.

A: Given curve is f(x,y) = x^2+y^2+xy-6y  Find critical points

Q: 3x4 – 4x3 – 12x² + 18 f(x, y) = 12(1+ 4y²)

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Q: Find the quadratic function f (x) = ax2 + bx + c that goes through (0, 1) and has a local minimum at…

A: Given: The quadratic function fx=ax2+bx+cpasses through the point 0,1 and has local minimum at 1,-1,…

Q: The function f(x, y) = 2x² + 4y² + 2x³ has a local maximum at the point (0, 0). Select one: O True O…

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Q: f(x) = 3 x4-4 x3 -12 x2+1, has local minimum at x = OA. OB 2- OC. OD.

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Q: Find the maximum value of  f(x,y)=3xy(5−10x−5y) over the triangle with vertices (0,0), (1/2,0) and…

A: Given :            f(x, y)= 3xy(5-10x-5y)            Vertices (0, 0) (1/2, 0) and (0, 1)

Q: Calculate the maximum and minimum of the function f (x,y) = xy subject to the condition x2 + y2 = 1

A: To find the optimal solution, we will use Lagrange multiplier method. The Lagrangian function is…

Q: Find and classify the critical points of the function f(x, y) = x²y+ 4xy – 2y².

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Q: Find the maximum and minimum values of the function f(x, y) = e²Y subject to + y° = 16

A: Given data: The expression for the first function is f(x, y)=exy. The expression for the second…

Q: Determine the coefficients a, b, c, and d, so that the curve y = ax' + bx² + cx + d have critical…

A: Since you have asked multiple questions, as per our policy we will answer first question. Please…

Q: Show that the function no-f 0, z = 0 f(2) = { – y* z#0 x2 + y? x² + y² is not differentiable at z =…

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Q: Find the maximum and minimum values of the function f(x, y)-xy subject to g(x, y) = x² + xy + y² =…

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Q: Find all points (x,y) where f(x.y) has a possible relative maximum or minimum. f(x.y) = x* - 32xy +…

A: Solution:Given thatfx,y=x4 -32xy+8y2-10we have to find all points x,y where fx,y has a possible…

Q: Find the critical point/s of the function f(x,y) x³+2xy-2x-4y

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Q: Find and classify the critical points of the function f(x,y) = x²y+ 4xy – 2y²

A: The given function is f(x,y) =x2y+4xy-2y2.

Q: (b) Find all stationary (critical) points of the function g(x, y) = x³ + y³ + 3x? + 3y + 3x + 3xy +…

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Q: The function f(x, y) = -2x² + 4y² - 12 has a local maximum at the point (0,0). Select one: O True…

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Q: Find the local minimum value of f(x, y) = 4 + x1 + yll – 11xy. 11 11

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Q: Where does the function f(x,y)=3 − 10x + 12y − 5x2 − 6y2 have a critical point?

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Q: Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular…

A: Given:- The function is, f(x,y)=3xy-3x-6y+1on the closed triangular region whose vertices are (0,0),…

Q: Consider the function f(x, y) = e^(10x - x^2 -10y - y^2). Find and classify all critical points of…

A: The given question can be solved as shown in step 2.

Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

Q: for the function f(Z) z²-2z find the (z+1)° (2 t4) residues at singular points.

A: The residue of f(z) is solved below

Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: Let f(x,y) = 5x² + 6y² + 3xy – 5x – 8y + 36 What is the first coordinate of the critical point?

A: Given data:   The given expression of the function is f(x,y)=5x2+6y2+3xy-5x-8y+36.     Equate the…

Q: Find the relative maximum and minimum values. f(x,y) = x° +y° - 3xy

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Q: 5. Find the absolute maximum and absolute minimum values of f(x, y) = 3xy-3x– 6y+1 on the closed…

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Q: For the function f(x,y) = –2x² – 3xy – y? – 3x, does the critical point (6, –9) correspond to a…

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Q: Does the function f(r,y) = e-(z²+y°) achieve an absolute minimum on D= R²? %3D

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Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

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Q: The function f(x, y) = x² + 4y2- 2x + 8y-1 has a local minimum at the point (-1, 1). Select one: O…

A: We will use first order derivative to find critical point.  If given point is critical point, then…

Q: If x² + y² < z < 1, find the maximum and minimum of the function u(x, y, z) = x + y + z

A: We have to find the maximum and minimum of the function.

Q: Find the maximum value of J (x) f(x) = V1 + x² on the indicated interval. [0,2]

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