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Subsections
The purpose of this lab is to acquaint you with using Maple to compute
partial derivatives.
To assist you, there is a worksheet associated with this lab that
contains examples. You can copy that worksheet to your home directory with the following command, which must be run in a terminal window, not in Maple.
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.
For a function of a single real variable, the derivative
gives information on whether the graph of is increasing or
decreasing. Finding where the derivative is zero was important in
finding extreme values. For a function of two (or more)
variables, the situation is more complicated.
A differentiable function, , of two variables has two partial
derivatives:
and
. As you have learned in class, computing partial derivatives is
very much like computing regular derivatives. The main difference is
that when you are computing
, you must treat
the variable as if it was a constant and vice-versa when computing
.
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.
- 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?
- Given:
- a)
- Find the tangent plane at .
- b)
- Plot the function and the tangent plane over the intervals
and
.
- There is only one point at which the plane tangent to the surface
is horizontal. Find it and plot it along with the function on the same graph. Be sure to use axes so that you can rotate the graph and see that the tangent plane is horizontal.
Next: About this document ...
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Dina Solitro
2006-03-24