Question: (a) The cubic function f(x) = x(x 2)(x 6) has three distinct zeros: 0, 2, and 6. Graph f and its tangent lines

(a) The cubic function f(x) = x(x – 2)(x – 6) has three distinct zeros: 0, 2, and 6. Graph f and its tangent lines at the average of each pair of zeros. What do you notice?
(b) Suppose the cubic function f(x) = (x – a) (x – b) (x – c) has three distinct zeros: a, b, and c. Prove, with the help of a computer algebra system, that a tangent line drawn at the average of the zeros a and b intersects the graph of f at the third zero.

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a fx xx2x 6 x 8x 12r fx 3x 16x 12 The average of the first pair of zeros is 022 1 At z 1 the slope o... View full answer

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