The discriminant ƒxx ƒyy - ƒxy 2 is zero at the origin for each ofthe following functions, so the Second Derivative Test fails there.Determine whether the function has a maximum, a minimum, orneither at the origin by imagining what the surface z = ƒ(x, y)looks like. Describe your reasoning in each case. ƒ(x, y) = x2y2

Q: The slope of the surface z = xy² in the x-direction at the point (2, 3) is _____, and the slope of…

A: Given:z=xy2   x-directionat the point 2, 3 y-directionat the point 2,3

Q: (a) Find an equation of the tangent plane to the surface of z = ye(3ry-y²) at (-1, –3, –3). (b)…

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Q: Find an equation of the tangent plane to the surface z = x^3- y^2 + 12x + 2y at the point (1, 2, 5).

A: Given: z = x^3- y^2 + 12x + 2y (1, 2, 5)

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 21, (1, 4,…

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Q: Find the equation of the tangent plane to the surface defined by the function f(x, y) = x³…

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Q: Given a surface f(x,y) = 0x + (4)y. Find the derivative in the direction of v = at the point (6,…

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Q: 6. Find the equation of the tangent plane to the surface: ==√√4-x²-2y², at (1,-1, 1)

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Q: 4. Find an equation of the tangent plane to the surface z = xy+8 at the point (1,1,-10) xy-2x

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Q: 4. Find the equation of the tangent plane to the surface Z = = 5tan(x) – sin(3y) at the point (xoyo)…

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Q: ( The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the…

A: Introduction: A real-valued function formed on a closed or bounded interval can have its absolute…

Q: 1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).

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Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

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Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 3 at the given point( 2, 1, 8).

A: Known fact: Let F(x,y,z) be the surface which is differentiable at P(x0, y0, z0). then the equation…

Q: #5. Find an equation of the tangent plane to the surface with the equation 12x z = x²y*. y at the…

A: The given equation of the surface: z=x2y4-12xy Therefore: f(x, y)=x2y4-12xy Now:…

Q: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given point (2, 2, 8)…

A: To Determine: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given…

Q: The discriminant ƒxx ƒyy - ƒxy 2 is zero at the origin for each of the following functions, so the…

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Q: Find the orthogonal trajectories for the families of curves y+x^2 = w where w is a parameter

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Q: Find equation of the tangent plane to the given surface at the specified point. 5x^2+3y^2+8z^2,…

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Q: . Use the second-derivative test for local extrema (: extrema for the function. Identify whether the…

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Q: Find the equation of the tangent plane to the surface y = 2a2- z2 at the point (0,-1, 1)

A: Here is the solution

Q: Given a surface f(x,y) = -2x² + (5)y². Find the derivative in the direction of v = at the point (7,…

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Q: 2. Set up the formulation to find the surface generated when the curve y=x is revolved about the…

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Q: Find an equation of the tangent plane to the surface z = In(x - 2y) at the point (3, 1,0) %3D

A: Given that, z = ln (x - 2y) we have to find the equation of tangant at point (3, 1, 0).

Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

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Q: A bug crawls on the surface z = x2 - y2 directly above a path in the xy-plane given by x = ƒ(t) and…

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Q: ( The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the…

A: Given that the discriminant fxxfyy−fxy2 is zero at the origin for each of the given function. a…

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: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

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Q: Find the equation of tangent plane to the surface x^2 + 2y^2 + 3z^2 = 21 which is parallel to the…

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Q: 4. Find an equation of the tangent plane to the surface z=- xy+8 at the point (1,1,-10) ху — 2х

A: Equation of tangent plane is: {df(x0,y0)/dx} (x-x0)+{df(x0,y0)/dy} (y-y0)-(z-z0)=0

Q: Let C be the curve on the xy-plane that is the projection of a horizontal cross-section of the…

A: Given surface is,yz=ln(x+z) zxy=1x+z(1+zx)y-1x+zzx=1x+zzx=1y(x+z)-1 Take the derivative with respect…

Q: Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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Q: Find the points on the graph of the function f(x) = x^2 that are closest to (0, 2) in the xy-plane.…

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Q: Find the slope of the tangent in the positive y-direction to the surface z = 3x + 2y − 5exy at (3,…

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Q: 9) Find a point on the surface z = 8 – 3x2 – 2y² at which the tangent plane is perpendicular to the…

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Q: 7. Find the equation of the tangent plane to the surface: x +y² -z² 1 z, at (2, 1, 2)

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Q: Given a surface f(x,y) = -3x² + (3)y². Find the derivative in the direction of v = at the point (5,…

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Q: Find the plane tangent to the surface given by the function f(x, y) = (x² + y) sen(x - y) + 2x in…

A: Tangent plane  z= f(x0,y0)+fx (x-x0)+fy(y-y0)

Q: 3. Find an equation of the tangent plane to the surface z = 2xy + 4y xy-2x at the point (1,1,-6)

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Q: Find and classify (local maximum, local mi points of f(x,y) = x2 - x²y + 2y². Show all supporting…

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Q: Find an equation of the tangent plane to the given surface at the specified point. 3.  z = 2x2 + y2…

A: Given that: z = 2x2 + y2 - 5y, (1, 2, -4)

Q: 4. Find the equation of the tangent plane to the level surface x4 + yz – yz² + 5x = 0 at 3

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Q: 5. Are there any points on the graph of x2 – y² – 22 = 1 where the tangent plane is parallel to the…

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Q: Find the slope of the tangent line to the curve that is the intersection of the surface z=x² - y…

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Q: 1)Determine the equation of the tangent line to the intersection of the surfaces x²-y=0 and y+z²=16…

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Q: What is the maximum vertical distance between the line y = x + 29 and the parabola y = x² over the…

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Q: ( The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the…

A: 1 Given function is fx,y=x4y4. f0,0=0 In the neighborhood of 0,0, choose any a,b∈R2, a,b≠0. Hence,…

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: Find the equation of the tangent plane to the surface 4. =1 at the point 16 9. (1,-3,2) O a.…

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Q: What is the largest vertical distance between the graphs of the functions y = Vx and y = x² in the…

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