![]() In the next part of our studies, we use calculus to make general observations about families of functions that depend on one or more parameters. Think about the Pythagorean Theorem: it doesn't tell us something about a single right triangle, but rather a fact about every right triangle. Mathematicians are often interested in making general observations, say by describing patterns that hold in a large number of cases. The main topics of this section are also presented in the following videos: How can we construct first and second derivative sign charts of functions that depend on one or more parameters while allowing those parameters to remain arbitrary constants? Given a family of functions that depends on one or more parameters, how does the shape of the graph of a typical function in the family depend on the value of the parameters? Section 3.4 Using Derivatives to Describe Families of Functions Motivating Questions Population Growth and the Logistic Equation.Qualitative Behavior of Solutions to DEs.An Introduction to Differential Equations.Physics Applications: Work, Force, and Pressure.Area and Arc Length in Polar Coordinates.Using Definite Integrals to Find Volume by Rotation and Arc Length. ![]()
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