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, select Draw Tangent from the Calculus menu. If you have chosen to select the initial point and curve using the mouse, use the mouse or arrow keys to move the crosshairs to any point on a curve on the screen, then click or press enter to select it. The program will draw the tangent line and display the point selected and the slope on the status line as well as in the Printout window if it is on. 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.

If you have chosen to show the Draw Tangent Line dialog box (also true by default), it will appear now if it is not already on screen. This dialog box allows you to choose the equation for the tangent line, plus adjust the x and y coordinates. You can use it to "straighten up" the coordinate produced using the mouse, or to enter an entirely different coordinate. When entering new coordinates manually, you may either:

1. Enter a value for the independent variable (usually x) only, and leave the other one blank.
2. Enter a value for the dependent variable (usually y), and optionally an estimate of the independent variable. The program will solve the equation for the exact independent variable value for you. When the function is not one-to-one, there may be more than one solution for a given value, so you should always include the independent variable estimate to indicate which solution you want to use.

You can only find the exact tangent line for differentiable (i.e. those which do not include the int() or abs() functions) Cartesian and polar equations. At this time, there is no efficient way to produce accurate results for other curves (for parametric equations you will get a rough approximation based on the slope between the two consecutive points nearest where you clicked).

In addition, I do not recommend drawing tangent lines when using logarithmic graph paper (since, of course, straight lines are not straight with a logarithmic scale).

The input method for drawing tangent lines is adjustable using the Tangent Line Options dialog box.