cp /math/calclab/MA1024/Partials_start.mws ~/My_Documents

You can copy the worksheet now, but you should read through the lab before you load it into Maple. Once you have read to the exercises, start up Maple, load the getting started worksheet and go through it carefully. Then you can start working on the exercises.

The Maple commands for computing partial derivatives are `D`
and `diff`. The **Getting Started** worksheet has examples
of how to use these commands to compute partial derivatives.

- Compute the three distinct second order partial derivatives of

at the point using the**diff**command and then again using the**D**command. - Given the function

- a)
- Plot the function and the plane on the same graph. Use intervals
,
,
and don't use
`scaling=constrained`. - b)
- Find the derivative of in the plane.
- c)
- Graph the two-dimensional intersection of the plane and on the same graph.
- d)
- Does your two-dimensional graph look like the intersection from your three-dimensional graph? Be sure to use the same ranges to properly compare and rotate the 3-D graph.

- Find two points at which the plane tangent to the surface given by the function
is horizontal. Use Maple's
`solve`command to find one of them (it will only yield one solution even though there are infinitely many) and use Maple's`fsolve`command to find another critical point in the ranges and . Find both tangent planes and plot them along with the function on the same graph over the intervals and . Rotate the graph so that you can see that the tangent planes are horizontal.

2008-03-26