![]() These can be important in applications such as identifying a point at which maximum profit or minimum cost occurs or in theory such as characterizing the behavior of a function or of a family of related functions.Ĭonsider the simple and familiar example of a parabolic function such as \(s(t) = -16t^2 32t 48\) (shown on the left of Figure3.1 below) that represents the height of an object tossed vertically: its maximum value occurs at the vertex of the parabola and represents the greatest height the object reaches. In many different settings, we are interested in knowing where a function achieves its least and greatest values. How can the second derivative of a function be used to help identify extreme values of the function? How does the first derivative of a function reveal important information about the behavior of the function, including the function's extreme values? What are the critical numbers of a function \(f\) and how are they connected to identifying the most extreme values the function achieves? Section 3.1 Using Derivatives to Identify Extreme Values Motivating Questions Population Growth and the Logistic Equation.Qualitative Behavior of Solutions to DEs. ![]() An Introduction to Differential Equations. ![]()
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