with detailed solution

1. [10 pts] Identify and sketch the quadric surface 9x2 + 32 - 922 - 54x - 4y - 542 + 4 =0. Use a computer algebra system to confirm your sketch. 2. [10 pts] Find all the third partial derivatives (if exist) of f(x, y, z) = x arctan(e"yz) + 3zzyz3 sec ( In x2 y). 3. [10 pts each] Identify any extrema of the function by recognizing its given form or its form after completing the square. Verify your results by using the partial derivatives to locate any critical points and test for relative extrema. a. f(x, y) = 25 - (2 - 2)2 - 32 b. f (x, y) = -22 - 32 + 10x +12y - 64