3. Consider the function A(x) = f cost sin³ tdt for x in [0, 2π]. Calculate A'(x), determine the intervals of increase/decrease and the critical points of A on (0, 27), if they exist. • Compute A(). • Sketch the graph of A on [0, 2π] using the above computation and the following information: A"(x) < 0 if and only if x in [0, ) U (2, 4) U (5,2π].

7. Suppose that f(1) = 4 and f'(x) 1. Use MVT to show that f(8) <18.

In x 6. Let f be the function given by f(x) = for all x > 0. The derivative of f is given by f'(x) = (a) Write an equation for the line tangent to the graph of f at x = e“. (b) Find the x-coordinate of the critical point of f. Determine whether this point is a relative minimum, a relative maximum, or neither for the function f. Justify your answer. (c) The graph of the function f has exactly one point of inflection. Find the x-coordinate of this point. (d) Find lim f (x).