Q3: Find the local maximum, local minimum, and saddle points of the surface f (x, y) = %3D 2x3 – 3x2y – 12x2 – 3y? + 7. [12 Marks]

Q: Using Lagrange multiplier, find the minimum value of f(x,y) = 3x +ly on the circle x2 + y2 = 1. Give…

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Q: Find the maximum value of f(x,y,z)=2x+5y+13z on the sphere x²+y²+z²=36

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Q: Q4/ Find the abs.max cand abs, min Valuse of the Runctia Kcx, y) = I+xy-3x on the closed regen…

A: We have f(x, y) = 1+xy-3x ∂f∂x = y-3, ∂f∂x = 0, y-3 = 0, y = 3 ∂f∂y = x, ∂f∂y = 0, x=0 So one…

Q: Q2/Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

A: We can use the second derivative test to find the maximum, minimum and saddle points.

Q: Q1/ Find maximum,minimum ,and saddle point of the surface = x³y³ - 12x + 3y + 12.

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: Find the points on the surface x² + y² + z² = 4 farthest from the point (1,–1,1), 2 %D

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Q: Find minimum distance from the surface x² – y? – z² = 1 (Lagrange Multipliers) to the origin.

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Q: SET UP the necessary equations to find the point on the intersection of the surfaces x2 + 4y2 + 4z2…

A: The solution are next step

Q: Q3: Find the points on the surface x^2+z^2-6=0, closest to the origin.

A: The distance of the point on the surface is given by d=x2+y2+z2. To obtain the distance insert the…

Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A: Use Lagrange multiplies we find heighest point on the curve ofintersection of the surface cone:…

Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

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Q: Find the minimum of f(x,y) = 5x + 4y on the ellipsoid 6x2 + 4y2 = 3. Leave your answer correct to t…

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Q: Q 05: Find the relative Maxima and Minima by classifying the critical points of the given surface…

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Q: Classify and sketch the surface x − y2 − 4z2 = 0.

A: The surface is given as x-y2-4z2=0. Rewrite the equation x-y2-4z2=0 as follows. x-y2-4z2=0x=y2+4z2…

Q: Q2/ Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

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Q: Find and classify all the critical points of the surface with its equation z = 32°y – y° + 3z – 3y²…

A: Given: z = 3x2y - y3 + 3x2 -3y2 + 2

Q: Q3: Find the points on the surface x^2+z^2-25=0, closest to the origin.

A: Distance formula is d2=x2+y2+z2 .......(1) From the given equation z2=25-x2 ....... (2)

Q: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the positively oriented simple closed curve C for which the value of the line integral     (y3…

A: The line integral is  ∫C(y3 − y) dx − 9x3dy The expression for Green's theorem is  ∫CP(x,y) dx…

Q: Q1/ Find maximum,minimum,and saddle point of the surface Z = x³y³ 12x + 3y + 12.

A: Given :- z=x3 -y3 -12x+3y+12 Find:- Maximum, minimum and saddle point of the given surface

Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

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Q: Q1: Find the maximum and minimum point on the surface f(x,y)= 5xy-7x -y² +3x -6y +2

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Q: 4. What is the maximum value of f(x, y, z) = xyz for points (x, y, z) lying on the ellipsoid x² + 4…

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Q: (b)Let f(x, y) = /3x +2y. %3D Find the slope of the surface z = f(x, y) in the x-direction at the…

A: (b) Slope of z= f(x,y) in the y- direction at the point (4,2) Slope ofz in the y - direction means…

Q: 4. Parameterize the curve of intersection of the surfaces z = x² + y² and y² + (z – 1)² = 1.

A: parameterisation

Q: Find the minimum of f(x,y) = 4x + 3y on the ellipsoid 4x2 + 2y2 = 6. %3D Leave your answer correct…

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Q: Q4/Find the abs.max and abs.min valuse of the huctu f,y) = \+xy-3x on the cosol regen oounded by the…

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Q: Find the maximum value of f(x,y,z)=25x+3y+17z on the sphere x2+y2+z²=100

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Q: Q3. Find the point(s) on the surface xyz 1 closest to the origin. %3D

A: Given: To find the points on the surface xyz=1 is given as,

Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

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Q: :y² + z² — ² by first sketching at least three cross sections in each of the 4. Graph the surface 1…

A: A quadric surface is a graph of an equation in the three variables x, y and z in a three dimensional…

Q: Find the minimum distance from the point to the surface z = V7 - 2x – 2y. (Hint: To simplify the…

A: We need to find the minimum distance from the point A (-2,-2,0) to the surface z = 7-2x-2y…

Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

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Q: Q6) (Lagrange Multipliers) to the origin Find minimum distance from the surface r? – y – 2? =1

A: The solution is given below in the next step:

Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: Q3: Find the points on the surface x^2+z^2-16=0, closest to the origin.

A: The equation of the surface is x2+z2-16=0.

Q: Q/ Find the points have minimum distance from the origin to the surface. xyz²=1

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Q: Q1/ Find maximum,minimum OULE ,and saddle point of the surface Z = x³y³ - 12x + 3y + 12.

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Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0 ≤ x ≤ 1…

A: The formula for the surface area of the rotating object from the curve y=f(x) with the constraint…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0< x <1…

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Q: Find the maximum value of f(x,y,z)=9x+14y+29z on the sphere x2+y2+z²=25

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Q: Q2 Find the maXimum and minimum values of aFunction FCXS.2) = 8x+j+ 2 en the Surface x+y, z"=18 %3D

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Q: Q2/ Examine the following surface for maximum , minimum, and saddle points z = x3 – 3x2 – 4y² + 2

A: Take the first order and second-order partial derivatives of z with respect to x and y.

Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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Q: 4) Let h(x, y) = 2x² + y² – 2x²y. Find the absolute minimum and maximum values of the surface on the…

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Q: Q.2/ Test the following surfaces for maxima, minima and saddle point:- Z(x,y) = xy + 7x? – 12y°x? -…

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Q: Find the minimum distance from the point (0, 0, 4) to the surface  z = (1-2x-2y)^1/2   (Round your…

A: Solution:

Q: Q1/ Find maximum,minimum ,and saddle point of the surface Z = x³y³ - 12x + 3y + 12.

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…