What is a slope field of a differential equation?

1 Answer
Jul 4, 2015

This is basically a graphical representation of many derivatives of one function, including vertical shifts, illustrating how the solution to an indefinite integral involves all vertical shifts, "#+C#"


A slope field is a way of describing the function #f(x) + C# by tracing its derivative at multiple points within a viewing window, including all of its vertical shifts.

When you see a slope field like this, if you simply connect the dashes together and make a curve, you trace the curve itself at some #+C# shift. Each dash corresponds to a single derivative at some value of #x#.