2. For each problem, sketch the constraint curve g(x,y) = C along with a contour diagram for f(x,y). Then indicate the points on the constraint curve where f(x,y) attains maximum or minimum values. a.) ƒ(x,y) = x + 2y g(x,y) = 4x² + y² = 4 b.) f(x,y) = xy g(x,y) = x² + 9y² = 9 %3D c.) f(x,y) = x² + y? g(x,y) = 2x + y = 5

Q: Problem 1. Let H be a Hilbert space and T: H → H be a linear application. Suppose that (Tx, x) > 0…

A: Given Data: We have to show that , Deduce that L=0.

Q: The minimum value of the function f(x, y) = 8x² – 2y +1 subject to the constraint x + y = 1 is:…

A:

Q: Find the maximum and minimum values of f(x, y, z) = xyz subject to the constraint x² +2y²+3z² = 6.

A:

Q: Two ships pursue straight-line courses at steady speeds. At each time t (in hours, where 0 ≤ t ≤ 9),…

A:

Q: 3. A firm's profit is given by the function PROFIT = 1000B - 3x² – 4x + 2xy – 5y²+ 48y, where x…

A: Given the profit function of the firm is  P(x,y)=1000B-3x2-4x+2xy-5y2+48y where x denotes the level…

Q: Find the minimum value of f(x,y)=56x2+21y2 subject to the constraint x²+y²=16

A:

Q: Find the minimum of f(x, y, z)= x² + y² + z² subject to the two constraints x + y + z = 1 and 4x +…

A: Below is the procedure for lagranges multipliers method.

Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: min f(x. y) = (x – 4)² +y- 4)? subject to x+y<4 and x+3y <9 a. Discuss whether a solution exists for…

A:

Q: Geometrically represent the set A = {(x, y) ∈ R²| x ≥ 0 e x² + y² ≤ 4} Determine if the function…

A: Given: A=x,y∈R2|x≥0 x2+y2≤4 To Find: i. Geometrically represent the set Aii. Determine if the…

Q: Find a possible equation for the linear function g(x, y) shown in the graph below: g(x, y) = -3 -8.…

A: Given that, the contour diagrams.We need to find the equation of the linear function .One of the…

Q: Let f(x, y) = x² +9y2. Find the maximum and minimum values of f subject to the given constraint. (a)…

A:

Q: Determine the extreme values (minimum and maximum values) of f(x,y ) = 3xy subject to the constraint…

A:

Q: Find the maximum and minimum of the function f(x,y) : 1 subject to the x² + 2y² constraint x* +2x²y²…

A:

Q: Find the point where the function f(r, y) = r² + 4y² + 12 subject to the constraint z + y = 5 takes…

A: f=x2+4y2+12..............(1) the given constraint is  x+y=5 y=5-x................put it back in…

Q: ii) Prove that the straight line y = x is the curve giving the shortest distance between the points…

A:

Q: Find the absolute minimum of the function ƒ(x, y, z)=x² + 2y² +3z² subject to the constraints:…

A: subjected to constrain

Q: The graph shows the level curves of a function f(x, y) = 6x² + 6y² and a constraint function g(x,…

A: Given: The above graph shows the level curves of a function f(x, y)=6x2+6y2. And the constraint…

Q: Q. Find the absolute maximum and the absolute minimum of the function f (x, y) 2x2 + y² subject to…

A: