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Consider the function f(x) = 4x − x2 and the point P(2, 4) on the graph of f. Part (a) Graph f and the secant lines passing through P(2, 4) and Q(x, f(x)) for x-values of 3, 2.5, 1.5. Part (b) Find the slope of each secant line. Part (c) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(2, 4). Describe how to improve your approximation of the slope.

Consider the function f(x) = 4x − x2 and the point P(2, 4) on the graph of f. Part (a) Graph f and the secant lines passing through P(2, 4) and Q(x, f(x)) for x-values of 3, 2.5, 1.5. Part (b) Find the slope of each secant line. Part (c) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(2, 4). Describe how to improve your approximation of the slope.

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Consider the function f ( x ) = 4 x − x 2 and the point P ( 2 , 4 ) on the graph of f . Part (a) Graph f and the secant lines passing through P ( 2 , 4 ) and Q ( x , f ( x ) ) for x -values of 3 , 2.5 , 1.5 . Part (b) Find the slope of each secant line. Part (c) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P ( 2 , 4). Describe how to improve your approximation of the slope.

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