[b]Slope Field:[/b] With "show corners" enabled, drag points [color=#ff00ff]P1[/color] and [color=#ff00ff]P2[/color] to adjust the size of the region. Option exists to show the numerically-generated solution curve through point [color=#ff0000]A[/color], which may be dragged to any location on the plane.[br][br][b]Euler's Method:[/b] Drag point [color=#ff0000]A[/color] to change the initial condition, or enter its point coordinates in the input box.[br][br][b]Function Equation:[/b] Gives option to enter a function equation that is presumably thought to be a solution to the differential equation. Include a constant of integration "C" or "c" if desired. Alternatively, may be used to prove that entered function does [i]not [/i]solve the differential equation if the graph does not run parallel to the slopes in the field.[br][br]If you have a correct solution curve, drag point [color=#ff0000]A[/color] to various points along the curve to see how well Euler's Method does or does not approximate other values along the curve.[br][br]Can you develop any general observations of when Euler's Method tends to do a good job of approximating vs. when it does not do a good job?

Version below used for presentation at AP Annual Conference 2024, reflecting [url=https://apcentral.collegeboard.org/media/pdf/ap21-frq-calculus-bc.pdf]Free Response Question AP Calculus BC 5[/url] (and [url=https://apcentral.collegeboard.org/media/pdf/ap21-sg-calculus-bc.pdf]solutions[/url]).