Mistake Master
Mistake Master · AP Calculus · Unit 7 · Step-Through Animation
The Slope, Everywhere at Once
You'll learnto build a slope field out of one substitution repeated, to find its spine before plotting anything, and to settle a matching question with a coordinate pair instead of an impression.
A slope field answers one question at every point of the plane: if a solution passed through here, how steep would it be? The equation answers it with arithmetic, one point at a time, and the picture that results shows the whole family of solutions before a single one has been found. Find where the slope is zero first, and when two candidate equations look alike, stop looking and substitute a point where they disagree. Twelve short steps; press Next for each one.
Substitute a point, draw the segment, and let the field appear
Before you start
What you're looking at
A grid of points, each carrying a short segment whose slope is whatever dy/dx works out to there. The whole picture is one substitution repeated.
The question
Where do the segments lie flat, which way do they lean on either side of that, and does the answer change as you move sideways or upward?