(C) The distance is approximately 14(6) + 8(2) + 3(4).
(D)
(A) Selecting an answer for this question from your calculator graph is
unwise. In some windows the graph may appear continuous; in others
there may seem to be cusps, or a vertical asymptote. Put the calculator
aside. Find
These limits indicate the presence of a jump discontinuity in the function
at x = 1.
(B) We are given that (1) f ′(a) > 0; (2) f ′′(a) < 0; and (3) G′(a) < 0. Since
G′(x) = 2f(x) · f ′(x), therefore G′(a) = 2f(a) · f ′(a). Conditions (1) and (3)
imply that (4) f(a) < 0. Since G′′(x) = 2[f(x) · f ′′(x) + (f ′(x))^2 ], therefore
G′′(a) = 2[f(a) f ′′(a) +
(f ′(a))^2 ]. Then the sign of G′′(a) is 2[(−) · (−) + (+)] or positive, where
the minus signs in the parentheses follow from conditions (4) and (2).
(D) Since , it equals 0 for . When x = 3, c = 9; this
yields a minimum since f ′′(3) > 0.
(D) In the figure below, S is the region bounded by y = sec x, the y axis,
and y = 4.
