AB/BC 6. (a)
(c) The line tangent to the graph of A at x = 6 passes through point (6, A(6)) or (6, 9π). Since
A ′(x) = f (x), the graph of f shows that A ′(6) = f (6) = 6. Hence, an equation of the line is y
− 9π = 6(x − 6).
(d) Use the tangent line; then A(x) = y ≈ 6(x − 6) + 9π, so A(7) ≈ 6(7 − 6) + 9π = 6 + 9π.
(e) Since f is increasing on [0,6], f ′ is positive there. Because f (x) = A ′(x), f ′(x) = A ′′(x);
thus A is concave upward for [0,6]. Similarly, the graph of A is concave downward for
[6,12], and upward for [12,18]. There are points of inflection on the graph of A at (6,9π)
and (12,18π).