58.
59.
60.
61.
62.
63.
Part B
(D) Since h is increasing, h′ ≥ 0. The graph of h is concave downward for
x < 2 and upward for x > 2, so h′′ changes sign at x = 2, where it appears
that h′ = 0 also.
(C) I is false since, for example, f ′(−2) = f ′(1) = 0 but neither g(−2) nor
g(1) equals zero.
II is true. Note that f = 0 where g has relative extrema, and f is positive,
negative, then positive on intervals where g increases, decreases, then
increases.
III is also true. Check the concavity of g: when the curve is concave
down, h < 0; when up, h > 0.
(A) If , then
(D) represents the area of the same region as ,
translated one unit to the left.
(D) According to the Mean Value Theorem, there exists a number c in the
interval [1,1.5] such that . Use your calculator to solve the
equation for c (in radians).
(E) Here are the relevant sign lines:
