V X C poor005/mod_resource/content/6/MATH209-Assignm A : 6 / 7 | - 157% +|8 Problem 5. Assume that single variable functions f(u), g(v) are smooth. Define the function w = f(u) + g(v), where u = ax + By and v = Bx tay, and a. B #0. a) Calculate Wer, Wyy and Wry. b) Find an expression in the form: AWxx + BWyy + CWxy = 0. Determine A, B and C. 14 .C ENG 11:42 PM Partly cloudy ID US 2023-10-061 WC Paniy cloudy + Problem 6. This problem deals with global minimization and maximization. As we've learned in lectures7 a continuous function f (z, y7 z) attains its maximum and minimum in any bounded and closed subset S2 of R3. These maximum and minimum points can occur either inside 9, which, if f is smooth7 is captured by the equation Vf=07 or on the boundary bnd(Q). The maximum and minimum of f on bnd() can be addressed using the Lagrange multiplier method. Now7 determine both the maximum and minimum values of the function f =my+ yz+z$ Within the region dened by the coordinate planes 23:07 y=07 2:0, and the plane 13+ y+ z: 17 restricted to the rst octant. 11:43 PM 2023710706 0