given the quadratic form h(x,y,z) = 3x^2 +3xy - 2y^2 + 3xz -4z^2 if a function...
given the quadratic form
h(x,y,z) = 3x^2 +3xy - 2y^2 + 3xz -4z^2
if a function g(x,y,z) is = h(x+3,y+2,z-5) and has an origin that is a critical point for h(x,y,z) find a critical point for g(x,y,z) while not calculating one, also is it a minimum or a maximum and is it unique?
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given the quadratic form
h(x,y,z) = 3x^2 +3xy - 2y^2 + 3xz -4z^2
if a function...
1. Consider the linear map f R3R4 defined by f(x, y,z) (x+y+ z, 2x +4z,3x +...
1. Consider the linear map f R3R4 defined by f(x, y,z) (x+y+ z, 2x +4z,3x + 2y +4z, 5y - 5z) a.) Find the matrix representing f (5pts) b.) Determine (i) ker(f) (2pts) (ii) Range(f) (2pts) and (i) dim(f) (lpt)
Let w=?3xy?4yz?3xz,x=st,y=est,z=t2 (1 point) Let Compute dw os ot
Let w=?3xy?4yz?3xz,x=st,y=est,z=t2
(1 point) Let Compute dw os ot
Find the maximum and minimum of the objective function: F =3x+2y subject to constraints: x >...
Find the maximum and minimum of the objective function: F =3x+2y subject to constraints: x > 0 y > 0 x + 2y < 4 x - y<1 Maximum value = 8, at point (0,4) Minimum value =0, at point (0, 0) Maximum value = 8, at point (8/3, 0) Minimum value =0, at point (1, -3/2) Maximum value = 8, at point (2, 1) Minimum value =0, at point (-2/3, 1) Maximum value = 8, at point (2, 1)...
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f(z, y) at the origin. Estimate...
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f(z, y) at the origin. Estimate the error in the approximation if |x| < .1 and |y| < .1 e-2y 1+n2
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f(z, y) at the origin. Estimate the error in the approximation if |x|
2. Define a function g: R3 +R by g(x, y, z) = 2x2 + y2 +...
2. Define a function g: R3 +R by g(x, y, z) = 2x2 + y2 + x2 + 2xz – 2y – 4. (a) Find all the critical points of g. (b) Compute the Hessian H, of g. (c) Classify the critical points of g. (d) The surface g(x, y, z) = 0 is an ellipsoid . Use the method of Lagrange multipliers to find the maximum value of the function (5 marks) (5 marks) (5 marks) f(x, y, z)...
z -1 2+32 subject to x*y . Find the maximum and minimum values of f(x, y,z) x + 2y and x-y +2z + 2. z -1 2+32 subject to x*y . Find the maximum and minimum values of f(x, y,z) x + 2y and x-y...
z -1 2+32 subject to x*y . Find the maximum and minimum values of f(x, y,z) x + 2y and x-y +2z + 2.
z -1 2+32 subject to x*y . Find the maximum and minimum values of f(x, y,z) x + 2y and x-y +2z + 2.
Find the extreme values of the function subject to the given constraint. f(x y, z)=x+2y-2z x2...
Find the extreme values of the function subject to the given constraint. f(x y, z)=x+2y-2z x2 + y2 + 22-9 Maximum: 9 at(1, 2, -2); minimum: -9 at (-1 -2.2) Maximum: 1 atil -2 -2); minimum: -1 at (-1 2. 2) Maximum: 8 at (2.1, -2): minimum: -8 at (-2-1. 21 Maximum: 1 at (-1-2-3); minimum: -1 at(1.2.3
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point (17) Consider the function f tha...
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point
find the maximum value of z=6x-3x^2+2y (subject to y-x^2=2 if condition changes to y-x^2=3, how much...
find the maximum value of z=6x-3x^2+2y (subject to y-x^2=2 if condition changes to y-x^2=3, how much will z increase?
1. Consider the linear map f R3R4 defined by f(x, y,z) (x+y+ z, 2x +4z,3x + 2y +4z, 5y - 5z) a.) Find the matrix representing f (5pts) b.) Determine (i) ker(f) (2pts) (ii) Range(f) (2pts) and (i) dim(f) (lpt)
Let w=?3xy?4yz?3xz,x=st,y=est,z=t2
(1 point) Let Compute dw os ot
Find the maximum and minimum of the objective function: F =3x+2y subject to constraints: x > 0 y > 0 x + 2y < 4 x - y<1 Maximum value = 8, at point (0,4) Minimum value =0, at point (0, 0) Maximum value = 8, at point (8/3, 0) Minimum value =0, at point (1, -3/2) Maximum value = 8, at point (2, 1) Minimum value =0, at point (-2/3, 1) Maximum value = 8, at point (2, 1)...
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f(z, y) at the origin. Estimate the error in the approximation if |x| < .1 and |y| < .1 e-2y 1+n2
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f(z, y) at the origin. Estimate the error in the approximation if |x|
2. Define a function g: R3 +R by g(x, y, z) = 2x2 + y2 + x2 + 2xz – 2y – 4. (a) Find all the critical points of g. (b) Compute the Hessian H, of g. (c) Classify the critical points of g. (d) The surface g(x, y, z) = 0 is an ellipsoid . Use the method of Lagrange multipliers to find the maximum value of the function (5 marks) (5 marks) (5 marks) f(x, y, z)...
z -1 2+32 subject to x*y . Find the maximum and minimum values of f(x, y,z) x + 2y and x-y +2z + 2.
z -1 2+32 subject to x*y . Find the maximum and minimum values of f(x, y,z) x + 2y and x-y +2z + 2.
Find the extreme values of the function subject to the given constraint. f(x y, z)=x+2y-2z x2 + y2 + 22-9 Maximum: 9 at(1, 2, -2); minimum: -9 at (-1 -2.2) Maximum: 1 atil -2 -2); minimum: -1 at (-1 2. 2) Maximum: 8 at (2.1, -2): minimum: -8 at (-2-1. 21 Maximum: 1 at (-1-2-3); minimum: -1 at(1.2.3
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point
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