K = number 9

1 Given the function f(x,y) = Kx* + x2y2 + y^, find all the first order and second order partial derivatives. (6 marks) 2 Given the function f(x,y) = Ksin(xy2), find the first order Taylor series expansion about the point 65.1). (8 marks) 3 Find the stationary points of f(x,y) = 3x3 + y3 - 9x - 12y + K, and classify them as maximum, minimum or saddle points. (13 marks) 4 Find the extrema of f(x,y) = 2x2 + y2, subject to g(x,y) = x + y +1 = 0. [6 marks] 5 Find the volume of the solid bounded by the planes x = 0, x = 1, y = 1, y = 2, z = 0 and the surface z = f(x,y) = R(x + 2xy). [9 marks] Page 1 of 2