The contour plot of a function f is shown below a Give the a

The contour plot of a function f is shown below: a) Give the approximate coordinates of all local maxima (if any exist). b) Give the approximate coordinates of all local minima (if any exist). c) Give the approximate coordinates of all saddle points (if any exist). d) Mark a point P on the contour plot that has the property that f_x(P) > 0, and f_y(P) = 0. e) At the point Q, draw nabla f. f) Consider points Q, R, S, and T. Among these points, at which point is ||nabla f|| the greatest, and at which point is |nabla f| the smallest? Briefly explain.

Solution

Ans-

Maxima uses an external plotting package to make the plots (see the section on Plotting Formats). The plotting functions calculate a set of points and pass them to the plotting package together with a set of commands. That information can be passed to the external program either through a pipe or by calling the program with the name of a file where the data has been saved. The data file is given the name maxout_xxx.format, where xxx is a number that is unique to every concurrently-running instance of maxima and format is the name of the plotting format being used (gnuplot, xmaxima, mgnuplot orgnuplot_pipes).

There are to save the plot in a graphic format file. In those cases, the file maxout_xxx.format created by Maxima includes commands that will make the external plotting program save the result in a graphic file. The default name for that graphic file is maxplot.extension, where extension is the extension normally used for the kind of graphic file selected.

The maxout_xxx.format and maxplot.extension files are created in the directory specified by the system variable maxima_tempdir. That location can be changed by assigning to that variable (or to the environment variable MAXIMA_TEMPDIR) a string that represents a valid directory where Maxima can create new files. The output of the Maxima plotting command will be a list with the names of the file(s) created, including their complete path.

If the format used is either gnuplot or xmaxima, the external programs gnuplot or xmaxima can be run, giving it the file maxout_xxx.format as argument, in order to view again a plot previously created in Maxima. Thus, when a Maxima plotting command fails, the format can be set to gnuplot or xmaxima and the plain-text file maxout_xxx.gnuplot (or maxout_xxx.xmaxima) can be inspected to look for the source of the problem.

The additional package draw provides functions similar to the ones described in this section with some extra features. Note that some plotting options have the same name in both plotting packages, but their syntax and behavior is different. To view the documentation for a graphic option opt, type ?? opt in order to choose the information for either of those two packages.

Categories:  Plotting

The plotting formats are the following:

Used to launch the external program gnuplot, which must be installed in your system. All plotting commands and data are saved into the filemaxout_xxx.gnuplot.

This format is not available in Windows platforms. It is similar to the gnuplot format except that the commands are sent to gnuplot through a pipe, while the data are saved into the file maxout_xxx.gnuplot_pipes. A single gnuplot process is kept open and subsequent plot commands will be sent to the same process, replacing previous plots, unless the gnuplot pipe is closed with the function gnuplot_close. When this format is used, the function gnuplot_replot can be used to modify a plot that has already displayed on the screen.

This format is only used to plot to the screen; whenever graphic files are created, the format is silently switched to gnuplot and the commands needed to create the graphic file are saved with the data in file maxout_xxx.gnuplot.

Mgnuplot is a Tk-based wrapper around gnuplot. It is included in the Maxima distribution. Mgnuplot offers a rudimentary GUI for gnuplot, but has fewer overall features than the plain gnuplot interface. Mgnuplot requires an external gnuplot installation and, in Unix systems, the Tcl/Tk system.

Xmaxima is a Tcl/Tk graphical interface for Maxima that can also be used to display plots created when Maxima is run from the console or from other graphical interfaces. To use this format, the xmaxima program, which is distributed together with Maxima, should be installed. If Maxima is being run from the Xmaxima console, the data and commands are passed to xmaxima through the same socket used for the communication between Maxima and the Xmaxima console. When used from a terminal or from graphical interfaces different from Xmaxima, the commands and data are saved in the file maxout_xxx.xmaxima and xmaxima is run with the name of that file as argument.