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Studying a Function

 Throughout the Calculus course we will be considering the behavior of a function.  The graphing calculator is a tool which allows us to visualize what is taking place with a set of points in a function (Section 20), the rate of change or slope of a function (Section 21), and the local and global behavior of a function (Section 22).

 Pierre Fermat Fermat posed further problems, namely that the sum of two cubes cannot be a cube (a special case of Fermat's Last Theorem which may indicate that by this time Fermat realized that his proof of the general result was incorrect), that there are exactly two integer solutions of x2 + 4 = y3 and that the equation x2 + 2 = y3 has only one integer solution. He posed problems directly to the English. Everyone failed to see that Fermat had been hoping his specific problems would lead them to discover, as he had done, deeper theoretical results.