Sketching direction fields

What you want to do is create a field of equally spaced coordinate points, and then evaluate the derivative at each of those coordinate points. Since the derivative is the same thing as the slope of the tangent line, finding the derivative at a particular point is like finding the slope of the tangent line there, which of course is an approximation of the slope of the actual function.

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Zero as an exponent

Any nonzero real number raised to the power of zero is one, this means anything that looks like a^ will always equal 1 if "a" is not equal to zero.

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Krista King