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The graph of a function is given. Determine the average rate of change of the function between the x coordinates of the two points on the graph of the function indicated in red. (You can click on the graph to enlarge the image.) Average rate of change = Z Find the slope of the secant line of the function f (x) = x2 + 4x 3 (a) On the interval [2, 0]. Answer: 2 (b) On the interval [2, 1]. Answer: 2 (c) On the interval [3, 2]. Answer: 2 (d) Use the slope of the secant lines computed in parts (b) and (c) above to estimate the slope of the tangent line of f(x) at x = 2. Answer: 2 Determine the average rate of change of the function f(t) = 4 + sint over the interval |0, T. Average rate of change = E Now determine the average rate of change of the function f(t) = 4 + sint over the interval - , Average rate of change =Find the slope of the secant line of the function f (x) = 3 tan(x) + 3 . 7:: (a) 0n the Interval ?, _ ] Answer: 2 (b) On the interval 4\" _ 77:] 3 ' 6 Answer: 2 (c) Use the slope of the secant lines computed in parts (a) and (b) above to estimate the slope of the tangent line of f (x) auxl\" _ 6' Answer: 2 Let f (x) = x2 + 3x. (a) Find the slope of the secant line joining P(1, f(1)) and @(5, f(5)). Slope of secant line: (b) Find the slope of the secant line joining P(3, f(3)) and Q(3 + h, f(3 + h)). Slope of secant line: E (c) Estimate the slope of the tangent line at P(3, f (3)). Slope of the tangent line : (d) Using the correct answer to part (c), find the equation of the tangent line at P(3, f(3)). y=