6. Find the absolute maximum and minimum values of fon D, where f(x,y)=x² – 2xy +2y...
6. Find the absolute maximum and minimum values of fon D, where f(x,y)=x² – 2xy +2y and D={(x,y)|0SX 33,05ys2.
Please answer number 6, and show and expkain your steps thank you 6. Find the absolute maximum and minimum values of fon D, where f(x,y)= x’ – 2xy +2y and D={(x,y)|05x53,0 sys2}. 7. Evaluate the integral [[ V«?+1d4, where D is the region bounded by the lines D y=0 and x =1, and the curve x= vy. You must evaluate this integral by hand and show all the steps that lead to your answer. Give the exact answer.
Find the absolute maximum and absolute minimum values of the function f(x, y) = 3x ^2 + 2y ^2 on the unit disk x^ 2 + y ^2 ≤ 1 , as well as the (x, y) coordinates where these extrema occur.
Question 8 (2 points) Find the absolute maximum and absolute minimum values of f (x, y) = 2x – 2xy + y² whose domain is the region defined by 0 < x < 4 and 0 <y <3.
Find the absolute minimum and absolute maximum values of the function f(x, y) = x2 + y2 – 2x – 2y + 12 on the triangular region R bounded by the lines x = 0, y = 0, and y = 5 – X. Explain your work step by step, in detail.
3. (a) Find the absolute maximum and minimum values for f(x,)s y on the rectangle (0, ) x 0.1. (b) Evaluate frrydA, where D is the shaded region drawn below 3. (a) Find the absolute maximum and minimum values for f(x,)s y on the rectangle (0, ) x 0.1. (b) Evaluate frrydA, where D is the shaded region drawn below
Find the absolute maximum and minimum values of f(x, y) = x² + 4y? – 164 – 4 on D: the set of points (x, y) that satisfy x2 + y2 < 25. Part 1: Critical Points The critical points of f are: (0,2) M Part 2: Boundary Work Along the boundary f can be expressed by the one variable function: f = f(y) = (49-y^2)+9y^2-36y-3 Σ List all the points on this side of the boundary which could potentially...
Question 1 (10 points). Determine the absolute minimum and maximum values of the function f(x, y) = 2x2 – 2xy + y2 – 2y +7 on the closed triangular region with vertices (0,0), (3,0), and (0,3). Be sure to show all calculations.
Find the absolute maximum and minimum values of f(x,y) = 2x + y4 on the set D = {(x,y) x2 + y2 <1}.
[2 points] Find the absolute maximum and minimum values of the function f(x, y) = e*- (x2 +2y2) on the domain D: {x,y) | x2 + y24}. 13. [2 points] Find the absolute maximum and minimum values of the function f(x, y) = e*- (x2 +2y2) on the domain D: {x,y) | x2 + y24}. 13.