Antiderivatives, Differential Equations, and Slope Fields

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Often, slope fields are used in lieu of actually solving differential equations.

Slide 14

Slope Fields

To construct a slope field, start with a differential equation. For simplicity’s sake we’ll use Slope Fields

Rather than solving the differential equation, we’ll construct a slope field

Pick points in the coordinate plane

Plug in the x and y values

The result is the slope of the tangent line at that point

Slide 15

Slope Fields

Notice that since there is no y in our equation, horizontal rows all contain parallel segments. The same would be true for vertical columns if there were no x.

Construct a slope field for .