		     FINDING THE DERIVATIVE OF A FUNCTION
To find the derivative of a function:
  1. Select the equation from the equation combobox
  2. Choose Derivative from the Calculus menu.
Graphmatica will perform symbolic differentiation on the equation to produce
its derivative, append the equation to the queue, and immediately graph it.

			    DRAWING TANGENT LINES
To calculate the slope of a curve and draw the tangent at a specific point:
  1. Select Tangent from the Calculus menu.
  2. Use the mouse or arrow keys to move the crosshairs to a point on any
     curve on the screen, then click or press enter to select it.
Graphmatica will draw the tangent line, and display the point selected and the
slope on the status line. The slope is calculated exactly for Cartesian and
polar equations. For parametric equations you will get a rough approximation
based on the slope between the points calculated nearest where you clicked.

These functions are only supported for Cartesian, polar, and parametric
equations. For relations containing y^2, the derivative is only found for the
positive root.  Derivatives and tangent lines cannot be found for equations
containing the functions int() or abs(), since these curves do not have
continuous derivatives.
					    Press PgDn for help on Integration
	       INTEGRATING TO FIND THE AREA UNDER/BETWEEN CURVES
To select a curve and region to integrate over graphically, choose Integrate
from the Calculus menu and then do one of the following:
 * With the keyboard, use the arrow keys to move the crosshair to the starting
   point on the curve you want to integrate. Press enter, then move to the x-
   value of the end of the range to integrate. Press enter again.
 * With the mouse, click on the starting point on the curve and drag the mouse
   to the endpoint of the region to integrate.
To find the area between two curves, position the crosshairs over the "bottom"
curve when you press enter the second time or release the mouse.

			      INTEGRATION DIALOG
To specify the endpoints more precisely, choose Integ Dialog in the Calculus
menu.  Respond to the prompts as follows to provide the needed information:
 1. Choose the equation to be on top from the first listbox.
 2. Choose the bottom equation from the next listbox (select the same one as
    before to find the area under a single curve).
 3. Type in the coordinate to use as the start of the region.
 4. Finally, type in the coordinate for the end of the region.

After you specify the region to integrate by either method, the program will
shade in the region used and display the numerical result in the status bar.
				    Press PgDn for help on Integration Options
			 SETTING INTEGRATION OPTIONS

To configure the way integrals are calculated and displayed, choose Integ
Options from the Calculus menu. There are two options you can control:

+ Integration method. Select from:
  Rects Above - Rectangles with edges completely above the curve (upper sums)
  Rects Below - Rectangles with edges completely below the curve (lower sums)
  Trapezoidal - Trapezoids with endpoints of edges on the curve
  Simpson's Rule - Segments bounded by quadratic approximation of the curve

+ Number of segments to calculate:
  This must be a positive integer, and if you use Simpson's Rule, it must be
  an even number. To a point, the higher the number, the more accurate the
  result will be. By default (and if you type "auto" instead of a number here)
  Graphmatica chooses the number of segments automatically to be half of the
  width in screen pixels of the area you selected.

If you choose a small enough number of segments and either the Rectangles or
Trapezoidal integration method, Graphmatica will actually draw each segment
individually rather than just shading the region. This can be helpful in
visualizing the calculations that go into finding the area.
				Press PgDn for help on Finding Critical Points
		       FINDING CRITICAL POINTS AND ZEROS
Graphmatica can find approximate solutions (zeros) and extrema (critical
points) for most smooth Cartesian functions. To calculate zeros and critical
points, first select an equation from the listbox, then choose the Critical
Pts option from the Calculus menu. This will show you a listbox full of all
extrema and zeros that could be found in the part of the graph on screen.

The listbox is divided up into three columns: type of point, solution, and
value of the function at that point.  The type of point is either Zero, Max,
or Min. The solution value is only printed for maxima or minima since for
zeros it is (of course) always zero.

There are two special items at the bottom of the listbox:
 [Find another]  Enter another guess to use as the seed for Newton's method.
		 This may be anywhere within the domain of the function; it
		 need not be on-screen. We will attempt to find the nearest
		 zero and maximum or minimum and add them to the listbox.
 [Done]          Select this or press ESC to dismiss the dialog.

CAUTION:  Although Graphmatica will not allow you to use this feature when it
can not find the first or second derivative of an equation, it cannot detect
when these are not smooth functions. This may impact the accuracy of results.
──────────────End of Calculus help. Press ESC to return to menu.──────────────
