Find all points (x.y) where f(x.y) may have a maximum or minimum. f(x,y) = - 3x + 5xy- 2y² +x+y

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

A:

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 maximum and minimum values of the function f(x, y) = 3y² + 2x² – 6y %3D in the region where…

A:

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

A:

Q: Show that the function z = f (x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given

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

A:

Q: Suppose that f(x, y) = 4x* + 4y* – xy Then the minimum is

A:

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 2x?.…

A: The given function is  f(x, y) = 2x2 - 5x - 3y + 5y2 To find the critical points of the function.

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

A:

Q: Find the local minimum value of f(x, y) = 4 + x° + y° – 9xy. ::

A:

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: Examine for minimum and maximum values of f(x,y,z)=2xyz-4xz-2yz+x^2+y^2+z^2-2x-4y+4z

A:

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: Find the absolute maximum and minimum of the function f(x,y) = 7y + 64x – 3 over the closed region…

A:

Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

A:

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: Find the maximum and minimum values of the function f(x, y) = xy onthe disk V = {(x, y) : x 2 + y2…

A: The given function is, fx,y=xyon the disk V=x,y:x2+y2&lt;1 fx=λgxfy=λgygx,y=1…

Q: find the critical point and classify the function f(x,y)= x3 +y3 - 6xy

A:

Q: Find the Maximum and Minimum values of f(x, y,z) x +3y subject to the constrains x'+4y +z-36.

A: According to question,Given function,fx, y, z = x2 + 3y2,           ....1subject to the…

Q: Suppose that f(z, y) = e-2-2y –2z+y Then the maximum is

A:

Q: Find the critical point of the function: f(x, y) = 4x2 + 2y2 − xy + x

A: we have given a function f(x, y)  We have to find the critical point

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) 3x? – 7x…

A:

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 the local minimum value of f(z, y) = 4 + x² + y7 – 7xy.

A: Explanation of the answer is as follows

Q: (c) Find the minimum and maximum value of f(x, y, z) = xy + yz.

A: Given: The function fx,y,z=xy+yz   To find: The minimum and maximum value of the given function

Q: Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 + y2 + z2 < 1.…

A: fx,y,z=2xyz on the unit ball x2+y2+z2≤1 gx,y,z=x2+y2+z2-1 ∇f=∂f∂x,∂f∂y,∂f∂z ∇g=2yz,2xz,2yx…

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

A:

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 4x² 5x…

A:

Q: st, enter DNE.) f(x, y) = x² + y² + 4x 10y6 minimum maximum point (x, y, z) = (x, y, z) = (x, y, z)…

A:

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

A:

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 critical point (xo, yo) of the function f(x, y) = 2x2 + 2xy + y? + 2x – 3.

A: Consider both the image for the solution.

Q: Find the absolute maximum and minimum values off on D, where f(x, y) = x – 2xy+2y and D={(x,…

A:

Q: Suppose that f(1, y) = 2z² + 2y – zy Then the minimum is

A: Given: fx,y=2x4+2y4-xy We need to find the minimum value of the given function.

Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

A:

Q: Find the maximum value of f on the region shown, subject to the constraint g (x, y) = c . At what…

A: a. The maximum value of f is 4. The point at which the maximum occurs is (0, 4).

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

A:

Q: Show that the function z = f(x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given a function in two variablesz=fx,y=x3-3x2-4y2+2

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

A:

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

A:

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

A:

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: Find the relative maximum and minimum values. f(x.y)=x +xy+y° 28y + 261

A:

Q: 2 f(x, y) = x² + 3xy

A:

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

A:

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) 4x? – 4x…

A:

Q: Find the relative minimum value for the function: f(x,y) = e(5x2+8y2+4).  those 2's are "squares"

A:

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

A:

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.