Given f(x) = x² + 3x + 9, find the average rate of change of f(x) over each of the following pairs of intervals. (a) [1.9, 2] and [1.99, 2] average rate of change over [1.9, 2] average rate of change over [1.99, 2] (b) [2, 2.1] and [2, 2.01] average rate of change over [2, 2.1] average rate of change over [2, 2.01] (c) What do the calculations in parts (a) and (b) suggest the instantaneous rate of change of f(x) at x = 2 might be? LO

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