Slope of a Tangent Line Sketch the graph of the function
(a) Find the slope of the line joining (4, 2) and (9, 3). Is the slope of the tangent line at (4, 2) greater than or less than this number?
(b) Find the slope of the line joining (4, 2) and (1, 1). Is the slope of the tangent line at (4, 2) greater than or less than this number?
(c) Find the slope of the line joining (4, 2) and (4.41, 2.1). Is the slope of the tangent line at (4, 2) greater than or less than this number?
(d) Find the slope of the line joining (4, 2) and (4 + h, f(4+h)) in terms of the nonzero number h.
(e) What is the slope of the tangent line at (4, 2)? Explain how you arrived at your answer.
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