Curve Sketching
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.
- Some Curve Sketching - Practice problems with Some Curve Sketching.
- What are all of the graphical features of a function?
- How do you sketch the graph of a function?
- How can you use asymptotes, local maximum and minimum values, inflection points, critical points, and concavity to sketch the graph of a function?
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Staff Review
This video starts off with an excellent summary / review of graphical features of functions, including increasing / decreasing behavior, concave up / concave down, horizontal asymptotes, vertical asymptotes, vertical tangents, cusps, and corners. Then, you wil learn how to sketch a graph by finding its features using methods we know. This video can get very complex, as almost everything you have learned so far in Calculus comes into play. If you understand this lesson, then you know you are doing well. -
