2a) Maximize and minimize the function f (x, y) = 1+ 4x + 2y – 2x² – y² on the triangle bounded by the lines x = 0, y = 0, and y = 6 – x, along with its interior. 2b) What property does the function...

Please solve part B


Extracted text: 2a) Maximize and minimize the function f (x, y) = 1+ 4x + 2y – 2x² – y² on the triangle bounded by the lines x = 0, y = 0, and y = 6 – x, along with its interior. 2b) What property does the function above have, and what properties does the region above have, that guarantee these maximum/minimum values will exist? (Hint: What I'm asking for here is how this problem satisfies the conditions of the Extreme Value Theorem.)