		     FINDING THE DERIVATIVE OF A FUNCTION

To find the derivative of a function, select it in the queue and then choose
Derivative from the Calculus menu.  Graphmatica will perform symbolic
differentiation on the equation to produce its derivative, add the resulting
equation to the queue, and immediately graph it.

Note that while the curve produced will always be correct, the equation of the
curve may not be in the simplest form, especially for complex equations. The
best way to check a derivative you found by hand is to overlay its graph with
the program's Derivative graph.

This function is only supported for Cartesian, polar, and parametric
equations. For relations such as equations containing y^2, the derivative is
only found for the function with the positive root. For equations with more
than one y, the derivative is found with respect to y instead of x.

Also, the derivatives of equations containing the functions int and abs cannot
be found, since these curves do not have continuous derivatives.


					  Press PgDn for help on Tangent Lines

			    DRAWING TANGENT LINES

At times you may be interested in knowing the slope of a curve at a given
point. Graphmatica will provide this information both numerically and
graphically about any curve on the screen with just a few clicks of the mouse.

To calculate the slope of a curve and draw the tangent line at a specific
point, first select Tangent from the Calculus menu. The cursor will change to
the crosshairs. Use the mouse or arrow keys to move 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 tangent line will be displayed only until you hide or delete the equation
it belongs to, clear the screen, or draw another tangent line.

Currently, you can only find the tangent line for differentiable Cartesian and
polar equations (i.e. those which do not include the int() or abs()
functions). For parametric equations you will get a rough approximation based
on the slope between the two consecutive points nearest where you clicked.
Support for other equation types and saving and restoring tangent lines along
with equation lists will be added to a future version of the program if enough
people request it.

					    Press PgDn for help on Integration
		  INTEGRATING TO FIND THE AREA UNDER A CURVE

Graphmatica can perform numerical integration to find the area under the curve
for any function on the screen. Just select Integrate from the Calculus menu.
The cursor will change to the crosshairs.

To select a curve and region to integrate over, 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. The interval you select is
   highlighted as you move the cursor.

The program will shade in the area that was found and display the numerical
result in the status bar, as well as send it to the printer if you have Print
Tables on. If you select a region under the axis, or highlight a region
above the axis from right to left, you will get a negative area.

The shading will be cleared as soon as you hide or delete the equation it
belongs to, clear the screen, or perform another integration. Integral regions
cannot be saved in equation list files at this time.
				    Press PgDn for help on Integration Options

			 SETTING INTEGRATION OPTIONS

You can choose between two methods of integration, as well as optionally
specify how many segments to divide the selected region into, to select more
accurate or faster computation. To modify the integration options, select Int
Options from the Calculus menu. Then choose between the Trapezoidal and
Simpson's Rule for the integration method. Simpson's Rule tends to produce
more accurate results, as long as the curve is smooth in the region you are
integrating. The Trapezoidal Rule may be slightly faster.

You can also set the number of segments to divide the region into when
calculating the area. This must be a positive integer, and if you use
Simpson's Rule, it must be an even number. The higher the number, the more
accurate the result will be, but the longer it will take to calculate it. 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 of the area you
selected in screen pixels.




──────────────End of Calculus help. Press ESC to return to menu.──────────────
