Calculus II, Spring 2013 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 10

1. Section 13.7: Problems 17, 35, 36, 37, 42, 45. Try to use the gradient analysis (i.e. sketch the gradient vectors to help you find the answer) in problem 37.

2. Section 13.8: Problems 7, 8, 25, 27, 29, 31. (Use the method of Lagrange Multipliers only).

3. (s13.7 extra1) Suppose that f_{x}(x, y) = 3x^{2} + 2x + 2y and f_{y}(x, y) = 2x + 2y. Does f has a local max, local min or a saddle point at (0, 0)? Hint: try the gradient analysis.

4. (s13.8 extra1) Find the equation of plane normal to the curve

\{ \begin{matrix}x^{2} + 2y^{2} + 3z^{2} = 6 \\ x + y + z = 3 \end{matrix}

at (1, 1, 1).

Hint: how is this plane related to the gradients of the two surfaces?