AP Calculus Question

2. Let f (x) be a twice differentiable function for all real numbers. The table on the right gives values of x 4 f (x) for selected points in the closed interval f (x) l S x S 1 1 . (a) Estimate f'(6) . Show the work that leads to your answer. I U) N "all M 11 (b) Evaluate I(x_] 2f'(x))dx . Show the work that leads to your answer. I] (c) Use a right Riemann sum with subintervals indicated by the data in the table to approximate the value of I f(x) ix . Show the I work that leads to your answer. (d) Suppose f'(2) = 4 and f'(x) > 0 for all xe [2, 5] . Use the line tangent to the graph of f at x = 2 and the secant line for the graph of fon [2, 5]to show that 2 S f(3) S 3