MA 1024 B '01 Practice Exam 2

- Compute the two first-order and three distinct second-order partial
derivatives of the function
.
- Compute the directional derivative of the function
at the point in the direction of the vector
.
- Find the equation for the tangent plane, or best linear
approximation, to the function
at the
point , .
- Show that the gradient of a function at a particular point is perpendicular to the level curve through this same point.
- Find the stationary points of the function
.
- Find the absolute minimum and maximum values of the function
on the square domain
,
.
- Sketch the contours of the function . Include and label in your sketch contours for , and
. You may restrict your attention to the rectangle
and
.
- Convert the expression

to cylindrical coordinates and spherical coordinates.

2001-12-04