1. The problem statement, all variables and given/known data Find the stationary points of the function: z = ax^2 + by^2 + c For each of the following sub-cases, identify any maxima and minima. i) a > 0, b > 0 ii) a < 0, b < 0 iii) a and b of opposite signs. 2. Relevant equations z = ax^2 + by^2 + c 3. The attempt at a solution Z'(x) = 2ax = 0 Z'(y) = 2by = 0 Z'(x) = Z'(y) => 2ax = 2by Solving for y: Y = ax/b Solving for x: X = by/a Z''(xx) = 2a Z''(yy) = 2b Z''(xy) = 0 Checking the condition [Z''(xx) * Z''(yy)] - (Z''(xy))^2 --> (2a*2b) - (0)^2 = 4ab. For i) where a and b are > 0 --> 4ab > 0 and 2a > 0 ---> Minimum For ii) where a and b are < 0 --> 4ab > 0 and 2a < 0 ---> Maximum For iii) where a and b are opposite --> 4ab < 0 --> Saddle Point Have I done this correctly? Because I can help thinking that I have forgotten something. I would really appriciate any help and input with regards to my attempted solution! - Thanks!