Slope of a Tangent Line One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point on the graph of (see figure). (a) Find the slope of the line joining and Is the slope of the tangent line at greater than or less than this number? (b) Find the slope of the line joining and Is the slope of the tangent line at greater than or less than this number? (c) Find the slope of the line joining and Is the slope of the tangent line at greater than or less than this number? (d) Find the slope of the line joining and in terms of the nonzero number Verify that and 0.1 yield the solutions to parts (a)(c) above. (e) What is the slope of the tangent line at Explain how you arrived at your answer.

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