Let f be the function given by f(x)=3sqrt(x-2).

Question

A) On the axes provided sketch graph of f and shade the region R enclosed by the graph f, the x-axis, and the vertical line x=8 (already completed just mentioned it for part B.)

B) Find area of the region R described in part (A).

C) Rather than using line x=8 as in part (A),consider the line x=k, where k can be any number greater than 2. Let A(k) be the area of the region enclosed by the graphs of f, the x-axis, and the vertical line x=k. Write and integral expression for A(k).

D) Let A(k) be as described in part (C). Find the rate of change of A with respect to k when k=8.