Previously, we studied how the slope of the tangent line, the derivative, at a point tells us whether the function is increasing, decreasing, or constant at that point. We will extend that relationship by exploring the relationship between the second derivative and the concavity of the function.
In this, our last Credit Unit, we will learn how to apply integration (antidifferentiation) to develop total cost, revenue, and profit functions using marginal cost, marginal revenue, and marginal profit functions. Lastly, we will explore a classical problem related to economics and many other fields - the area bounded by a curved function - by using Reimann Sums and then by using the Fundamental Theorem of Calculus.
Apply calculus to solve problems with confidence, persistence, and openness to alternate approaches.
Connect the graphical behavior, numerical patterns and symbolic representations of function and derivatives.
Recognize when and how to proficiently apply calculus tools to solve problems in business management, social sciences and and biological sciences.