Practice Set B
Calculus, Graphics, and Linear Algebra
Problems 2, 3, 5–7, and parts of 10–12 require the Symbolic Math Toolbox. The others do not.
1. Use contour to do the following.
(a) Plot the level curves of the function f(x, y) = 3y + y3 - x3 in the region where x and y are between -1 and 1 (to get an idea of what the curves look like near the origin), and in some larger regions (to get the big picture).
(b) Plot the curve 3y + y3 - x3 =5. (c) Plot the level curve of the function f(x, y)= y ln x + x ln y that contains the point (1, 1).
2. Find the derivatives of the following functions, and if possible, simplify each answer: