MA 1024 B '01 Practice Exam 2

1. Compute the two first-order and three distinct second-order partial derivatives of the function .

2. Compute the directional derivative of the function at the point in the direction of the vector .

3. Find the equation for the tangent plane, or best linear approximation, to the function at the point , .

4. Show that the gradient of a function at a particular point is perpendicular to the level curve through this same point.
5. Find the stationary points of the function .

6. Find the absolute minimum and maximum values of the function on the square domain , .

7. Sketch the contours of the function . Include and label in your sketch contours for , and . You may restrict your attention to the rectangle and .

8. Convert the expression

to cylindrical coordinates and spherical coordinates.

William W. Farr
2001-12-04