For the function f(x, y) = x + xy – 2xºys – 3y*, find the following:...
3. (28 points) Let f(x,y) = 2x3 - 6xy+3y- be a function defined on xy-plane. (a) (6 pnts) Find first and second partial derivatives of f. (b) (10 pnts ) Determine the local extreme points of f (max., min., saddle points) if there is any. (C) (12 pnts) Find the maximum and minimum values of f over the closed region bounded by the lines y = -x, y = 1 and y=r
Find f (x,y). f(x,y)= e - 4x + 3y A. fx(x,y)= -4 e - 4x OB. {x(x,y)= - 4 € -4x+3y OC. fx(x,y) = e -4x+3 OD. fx(x,y) = 3 e - 4x+3y
12 pts Consider the function f(x,y) = xy - 3x - 2y + 17x+y+37 and the constraint olx.1) -- 6x + 3y = 12. Find the optimal point of f(x,y) subject to the constraint (.). Enter the values of r, y. f(x,y), and below. NOTE: Enter correct to 2 decimal places. y = f(x,y); =
Find fx (x,y). f(x,y)= e - 4x + 3y O A. fx(x,y)= -4 e - 4x OB. fx(x,y) = -4 e - 4x + 3y O C. &x(x,y)= e = 4x+3 OD. &x(x,y)=3 € -4x+3y
Find the global maximum of 2 = f(x,y) = 3y - xy over the region bounded by y=x², y = 0, and x = 4.
For the function f(x,y)-In(x' + xy) find a) f
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
Consider the function f(x,y) = xy - 3x-2y2 + 17x + y + 37 and the constraint glx.v) = -6x + 3y - 12. Find the optimal point of f(x,y) subject to the constraint g(x.). Enter the values of, y. f(x,y), and below. NOTE: Enter correct to 2 decimal places y f(x,y) A-
Please describe the contour map and list important aspects of it, thanks! Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x, y) for which f(x, y) is a potential function, b) c) sketch a contour map of f (x, y) and, on the same figure, sketch F(x,y) (on R2). Comment on any important aspects of your sketch. Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x,...