Courses on khan academy are always 100% free. Start practicingand saving your progressnow: This calculus video tutorial explains how to find the relative extrema of a function such as the local maximum and minimum values using the first derivative. In this article, we will learn how to find the relative extrema of a function using the derivative tests and using graphs. We will also solve different examples to understand the steps for finding the relative extrema and for the clarity of the concept.
The web page explains the second derivative test, the first derivative test, and how to interpret the sign of the derivative. To determine if a critical point is a relative extrema (and in fact to determine if it is a minimum or a maximum) we can use the following fact. Fact suppose that \(\left( {a,b} \right)\) is a critical point of \(f\left( {x,y} \right)\) and that the second order partial derivatives are continuous in some region that contains \(\left( {a,b. Testing for relative extrema in cubic function.
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