cp /math/calclab/MA1024/Pardiff_start_D11.mw My_Documents

Another way to access the getting started worksheet is to go to your computer's Start menu and choose run. In the run field type:

\\filer\calclabwhen you hit enter, you can then choose MA1024 and then choose the worksheet

Pardiff_start_D11.mwRemember to immediately save it in your home directory. Once you've copied and saved the worksheet, read through the background on the internet and the background of the worksheet before starting 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

do the following:- a)
- Plot the function and the plane on the same graph. Use plotting ranges , , .
- b)
- Find the derivative of in the plane.
- c)
- Find the equation of the tangent
**line**at the point in the plane. - d)
- Graph the two-dimensional intersection of the plane and along with the tangent line at . Be sure to use and ranges that are consistent with your ranges in part a.
- e)
- Does your two-dimensional graph look like the intersection from your tree-dimensional graph?

- Given:

- a)
- Find all points on the graph where the tangent plane is horizontal.
- b)
- Find the equation of each horizontal plane and plot them on the same graph as the function . Use plotting ranges , .

2011-03-29