AP Calculus BC / Unit 7: Differential Equations
7.4 Reasoning Using Slope Fields
Notes
Match a slope field to an equation by checking where slopes are 0, positive or negative, and whether they depend on $x$, $y$ or both. A solution curve follows the segments through a given point.
Practice
A slope field has identical slopes along each horizontal row. The equation depends:
Same $y$, same slope.
In a slope field, slopes are positive above $y=2$ and negative below. Solutions starting near 2 tend to:
Above, they rise; below, they fall.
A solution curve through a point in a slope field must:
The segments show the slope of the solution.
Ready for more? Take the Unit 7 test.