Slope field: drag the corners P1 and P2 to adjust the size of the region[br][br]Euler's method: drag the [color=#ff0000]red point A[/color] to change the initial condition, or enter its point coordinates.[br][br]Notice that it's up to you to ensure that the Function Equation is the solution to the differential equation.[br]If your function doesn't run along or parallel to the slopes in the field, then it must not be a solution![br][br]If you have a correct solution curve, drag the [color=#ff0000]red point 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]).