5 for 5 Calculus BC Day 11

5 for 5: Calculus BC Day 11 The function f is continuous for all real values of x. A portion of the graph of the function f', the derivative of f, [-4, 8]. The graph of f is shown in the figure is shown above and consists of a semi circle and two linear pieces. BC1: Find the x coordinate of each critical point of f on the interval [-2, 8]. Classify each critical point as a local maximum, a local minimum, or neither for f. Justify your answers. BC2: Find lim S2 f' (t ) dt - 4 X -4 3(x - 4)2 -. Show the work that leads to your answer. BC3: Evaluate | cos( f'(x) ) f" (x)dx. BC4: For x 2 8, the function f' is defined by f' (x) =- 48 x4/3 . Evaluate | f' (x)dx or show that the definite integral diverges. BC5: (i) Consider the series > an where an = [f'(n)]P-1. Find all values of p where an converges. n = 8 n =8 (ii) Consider the geometric series M -3r", Find the value of r such that ) -3r = f"(3). n= 0 n=0