AB/BC 3.
(b)(c)(d)(e)AB 4.
(b)Part B
(a) The average value of .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).
Use the tangent line; then A(x) = y ≈ 6(x − 6) + 9π, so A(7) ≈
6(7 − 6) + 9π = 6 + 9π.
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).(a) (Review Chapter 3)
, when x = 4 then y = 4.
Verify that (4,4) is on the curve:
2(4)^2 − 4(4)(4) + 3(4)^2 = 32 − 64 + 48 = 16
Therefore, the point Q (4,4) is on the curve and the slope there
is zero.
(Review Chapter 3)