By minimizing the function ƒ(x, y, u, y) = (x - u)2 + (y - y)2 subject to the constraints y = x + 1 and u = y2, find the minimum distance in the xy-plane from the line y = x + 1 to the pa-rabola y2 = x.

Q: Find the minimum of f(x,y) = 2x2+3y2 subject to x2+y2=4.

A:

Q: We cannot plot the 4D graph (x, y, z, w) of a function of three variables w = f(x, y, z), but we can…

A: As per the question we are given the following trivatiate equation : w = x + z2 And we have to…

Q: Find the maximum and minimum points of the following: 1 1. y = vx- 2. у %3D х3 — Зх2 -

A: Given; 1) y=√x-1/√x 2)y=x3-3x2.

Q: find the intersection point between the line      X=1+2t {    y=2-t       Z=3 and the x+y-z=3…

A: The intersection point will be common to both the line and the plane. Therefore, substitute the…

Q: n F(x, y) = x² + 2y. A

A:

Q: Find the shortest distance between the lines i-(i+2j+k) + 2(i-j+â)and 7= 2i - j-k + 4(2i + j+ 2k)

A: The equation of the given lines are r→=i^+2j^+k^+λi^-j^+k^r→=2i^-j^-k^+μ2i^+j^+2k^ It is known that…

Q: 4 Suppose that f(x, y) = 3x¹ + 3y¹ − xy. Then the minimum value of f is

A:

Q: Find the minimum of f(x,y) = 2x2 + 3y2 subject to x2 + y2 = 4.

A: We have to find the minimum value.

Q: Suppose that f(x, y) = 2x² + 2y² - 2xy Then the minimum is

A: Given the function is:f(x,y)=2x4+2y4-2xy

Q: Find the maximum and minimum of f(x,y) = yx2 + y(y - 1)2 subject to x2 + y2 =1.

A:

Q: Consider the function f(x, y) = x ^3 + y ^3 + 3xy and the constraint (x − 3)^2 + (y − 3)^2 = 9.…

A:

Q: Find the extremum of​ f(x,y) subject to the given​ constraint, and state whether it is a maximum or…

A:

Q: Show that the line x + 1 =y/−1=(z − 2)/2 is in the plane 2x + 4y + z = 0.

A: Given equation of a line, x+1=y-1=z-22 And equation of a plane, 2x+4y+z=0

Q: Suppose that f(x, y) = 2x² + 2y¹ − 2xy Then the minimum is

A: Given function: f(x,y)= 2x4+2y4-2xy partially differentiating f w.r.t. x, ∂f∂x= 8x3-2y partially…

Q: Find points on the straight line segment joining (-3,-1) and (3, 2) wher the function f(x, y) = xy²…

A: Find equation of line joining two points

Q: find the maximum value of z = xy2 subject to 2x2 + y2=864;  x ≥ 0, y ≥ 0,

A: