In this lesson on curve sketching, we learn how to graph a function using the first and second derivatives, infinite limits, and limits at positive/negative infinity. We explore how the sign of the first and second derivatives indicate whether a function is increasing or decreasing and concave up or concave down. The lesson includes examples of how to apply these concepts to sketch the graph of functions such as f(x) = 5x³ - 3x⁵ and f(x) = x³/(x² - 3).
Graphing y = f(x) using the first and second derivatives, infinite limits, and limits at positive / negative infinity.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.