F(x,y)=x3-y3-2xy+6 find the local maximum and minimum

Q: Find the second-order partial derivative fxx ( x , y ) of the function f ( x , y ) = x 6y 4 -…

A: Given f(x,y)=x6y4-2x7y8+17x-y

Q: Find ∇f(x, y, z) for the function f(x, y, z) = x2 + y2 − 4z and find the direction of maximum…

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Q: Find the values of x, y, z at which f (x, y, z) = x2 + 4y2 + 5z2 - 6x + 8y + 3 assumes its minimum…

A: f(x, y, z)=x2+4y2+5z2-6x+8y+3   we have to find all points of x, y, z Taking, ∂f∂x=0, ∂f∂y=0 and…

Q: Find the absolute maximum and minimum of the function f(x,y) = 4y² + 18x – 18 over the closed region…

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Q: Find the linearization of the function f(x,y) = ln(x3y6) at the point (x0,y0) = (4, 3). Leave all…

A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

Q: The function f (x, y) = 2x + 3y + 9 - x2 - xy - y2 has a maximum at some point (x, y). Find the…

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Q: Find all points (x, y) where f(x, y) has a possible relative maximum or minimum.

A: We have to find the critical points for the function f(x,y)=-x2+2y2+6x-8y+5.

Q: The function f(x, y) = 2x² + y² – 3xy – 2x + y – 2 has one critical point. Find it, and determine if…

A: take the partial derivative with respect to x

Q: Find the maximum rate of change of f(x,y) =x²y+ /y at the point (1,1). In what direction does it…

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Q: Given f(x, y) = (3x – x2)(2y – y?). (a) Find all the critical points of the function. (b) Classify…

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Q: Find the gradient of f(x, y) = y ln x + xy2 at the point (1, 2).

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Q: Classify all the critical point(s) of f(x, y) = 22 + 6x? – 3y3 – 150.x. Find maximum and minimum…

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Q: Find the absolute maximum and absolute minimum values of the function f(x, y) 2x3 + 3xy + 2y %3D…

A: We have to find the absolute maximum and absolute minimum values of the function fx,y=2x3+3xy+2y3…

Q: 2. Given f(x, y) = 12x2x³ + 3y² + 6xy. (i) Find critical points of f. (ii) Use the second derivative…

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Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: f(x, y) = 2x2 + 3y2 - 4x - 1, x2 + y2 s 16 maximum minimum

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Q: Find the partial derivativef,for the functionf(x,y) - &x+y. 1,(x.y)- 17 1,(x.y) = Sx+y Sx ,(1.y) =…

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Q: Consider the function f(x, y) = 3x³ + 3xy² - 18x - y² Compute the stationary points of the function…

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Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

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Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

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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: Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and…

A: Given function is

Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: does not exist, enter DNE.) f(x, y) = x2 + y2 + 2x - 14y + 9 relative minimum (х, у, 2) - relative…

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Q: Find the absolute minimum and absolute maximum of f(x,y)=19−9x+13y on the closed triangular region…

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Q: Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y)…

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Q: Find the maximum and minimum values of f(x, y) = (x- y) e- + y)

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Q: Consider the function f(x, y) = y6 - 3x²y + 3x² Compute the stationary points of the function f(x,…

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Q: Find the critical points of f(x, y) = x³ – 6xy + y³. Use the second derivative test to classify each…

A: For the solution follow the next steps.

Q: Find the point where the function f(x,y, z) = x + 2y + 3z subject to the I takes on its minimum…

A: The given function is f(x,y,z)=x+2y+3z.

Q: Find the maximum rate of change of the function f(x, y) 3y5 x at the point (3,4)

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Q: Find the critical point (x_0,y_0) of the function f(x,y)=(√(x2+y2))+1.

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Q: f (x, y) = 3x^3 −9x+9xy^2. Use the second derivative test to classify the critical point (1,0) as a…

A: Recall: second derivative test : (i)  Firstly find critical points . i.e, fx(x,y) =0 and…

Q: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,…

A: To analyze the critical point (0,pi/4) of the given function of two variables

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: Find the orthogonal trajectories of x^2+y^2−2cy=0

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Q: Find the absolute maximum and minimum values of f(x, y)= 3+xy-x-2y on the closed triangular region…

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Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: Find the partial derivative for the function f(x,y)=√x+y3 f(xx,y)= f(x,y) = √8x + y² 33x √8x+y³ (y)=…

A: The given function is;  f(x,y)=sqrt(8x+y3).

Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 2y + 3z) at the point (−9, 6, 2) and the…

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 5z) at the point (- 1, 1, 2).

A: We have to find

Q: Find the critical point (x0,y0) of the function f(x,y)=(√(x2+y2))+1.

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Q: Find the maximum slope on the graph of f(x, y) = 2 sin(ry) at the point P(4, 0).

A: The given question can be solved as shown in step2.

Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: The functions f(x, y) = x 2 + y 2 and g(x, y) = x 2 - y 2 both have acritical point at (0, 0). How…

A: We have f(x, y)=x2 + y2 and g(x, y)=x2 - y2 By finding the partial derivatives fx=2x, fy=2y, gx=2x,…

Q: Find the maximum rate of change of f(x, y, z) = tan(7x + 3y + 6z) at the point (4, – 5, 2).

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

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Q: (b) Form the partial equation by eliminating function f from z = f(x?

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Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…