Write a single script which does each of the following in turn. Make sure you run the script in order to see the results (and possible errors!) before submitting it!
1. Plot the function f(x, y) = ∑∑x² + y² and assign the result to q1.
2. Plot the function f(x, y) = cos(x² + y²) / e^(x² + y²) and assign the result to q2.
3. Find the derivative ∂²/∂x∂y (x³y² / (x - cos(y))) and assign the result to q3.
4. Assign g(x, y) = xy / (x² + y²) and calculate f_yxx(1.2, 3.8) (triple derivative!) and assign the result to q4.
5. Assign f(x, y) = x - xy² + ∑y. Find ∇f(2, 9) and assign the result to q5. You'll need subs, too.
6. Find the directional derivative of f(x, y) = x/y + sin(xy) in the direction of u = 3i - 2j and assign the result to q6.
7. Find all critical points for f(x, y) = (y - 2) ln(xy). In Matlab ln is done with log. Assign the result to [q7x, q7y].
8. Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = xy² subject to the constraint x² + y² = 16. Assign the second-to-last line to [q8L, q8x, q8y] and the last line to q8f.