Curves That Obey Every Segment

You'll learnto sketch the solution through a given point in both directions, to find the flat rows that are solutions all by themselves, and to see why a curve that crosses one has stopped solving the equation.

A slope field is a page full of instructions, and a solution curve is what follows them. Every short line the curve passes has to be its tangent right there, and that single rule settles which way the curve goes, how it bends, where it ends up, and the one thing it can never do. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · A FLAT ROW IS A SOLUTION, AND A WALL · v2

a flat row is a solution, and nothing else may touch it

Before you start

What you're looking at

A field of short lines. Each one is the slope a solution must have at that spot, and here the field is given rather than drawn.

The question

Given the field and one point, what does the curve through that point do — to the left as well as the right, and in the long run?

Step 1 / 12