Because the derivative provides information about the gradient or slope of the graph of a function we can use it to locate points on a graph where the gradient is zero. Calculus and its applications is the most studentoriented applied calculus text. Exercises and problems in calculus portland state university. Pdf a deeper learning of the properties and applications of the derivative for the study of. Problem 21 find the rectangle of maximum perimeter inscribed in a given circle. Using the first derivative to distinguish maxima from minima. A reform approach to business calculus 23 global maxima and minima 94 the table below. The simple goal of this guide is to demonstrate how to. It loosely follows the treatment of stewarts calculus, seventh edition. All the numbers we will use in this first semester of calculus are. In this article, we explore the conditions of necessity or sufficiency of the criteria for determining the maxima and minima of a function. Jacobians maxima minima maxima and minima calculus. Differential calculus chapter 3 applications maxima and minima applications application of maxima and minima 21 24 solved problems in maxima and minima.
To identify maximaminima at this point either first derivative test or higher derivative test can be used. To download, select save target as from the dropdown menu. I have placed the the latex source files on my web page so that anyone who. Differential and integral calculus in charles rene reyneau. The worksheet will give students practice in using calculus to solve a wide. The second derivative is introduced in the module introduction to differential calculus. General method for sketching the graph of a function.
Maxima and minima without calculus by niven, ivan morton, 1915publication date 1981 topics maxima and minima. Pdf derivative, maxima and minima in a graphical context. Math 221 first semester calculus fall 2009 typeset. In a smoothly changing function a maximum or minimum is always where the function flattens out except for a saddle point. Maxima and minima without calculus pdf free download. Chalkboard photos, reading assignments, and exercises solutions pdf 3. Jay kerns december 1, 2009 the following is a short guide to multivariable calculus with maxima. You may download the pdf version of this file here. Pdf produced by some word processors for output purposes only. Examples functions with and without maxima or minima. Nuffield freestanding mathematics activity maxima and minima teacher notes. Maxima and minima mctymaxmin20091 in this unit we show how di. A maximum is a high point and a minimum is a low point.
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