Question

i just need help with these 2

HWK 07:Problem 7 Previous Problem List Next 1 point) Find the maximum and minimum values of the function f(o,)-34x-5 on the domain400 The maximum value of f(, y) is: 1199 Lust the pointlo) where the functlion attains ts maximum as an ordered pair, such as (6.3), or a list of ordered pairs if there is more than one point, such as(1.) (306,600,1199) The minimum value of f(a,) is: 715 as an ordered pair, such as (6,3), or a list of ordered pairs if there Is more than one point, such as (1.3), 4,7) (715,875,1195)

Answer 1

Given that f (x, y) = 2 x^2 + 3y^2 - 4x - 5 f_x = 2 * 2x + 0 - 4 - 0 f_x = 4x - 4 f_y = 0 + 3 * 2y - 0 - 0 f_y = 6y For critical point set fx = 0 and fy = 0 therefore 4 x - 4 = 0 4x = 4 x = 1 6y = 0 y = 0 therefore critical point (1, 0) Boundary of critical point because x^2 + y^2 = 400 y^2 = 400 - x^2 y = plusminus 400 - x^2 y = plusminus squareroot 400 - x^2 its end points is (negative 20, 0), (20, 0) \r\n because f(x, y) = 2x^2 + 3y^2 - 4x - 5 Plug y^2 = 400 - x^2 f = 2x^2 + 3 (400 - x^2) - 4x - 5 = 2x^2 + 1200 - 3 x^2 - 4x -5 f = negative x^2 - 4 x + 1195 Therefore dt/dx = negative 2x - 4 set dt /dx = 0, negative 2x - 4 = 0 x = 4/negative 2 x = negative 2 y plusminus squareroot 400 - (negative 2)^2 = plusminus squareroot 400 - 4 = plusminus squareroot 396