(D) At x = a, f ′ changes from increasing (f ′′ > 0) to decreasing (f ′′ < 0).
Thus f changes from concave upward to concave downward, and
therefore has a point of inflection at x = a. Note that f is differentiable at
a (because f ′(a) exists) and therefore continuous at a.
(C) We know that . Since S = .
(E) The equation of the tangent is y = −2x + 5. Its intercepts are and 5.
(D) See the figure. At noon, car A is at O, car B at N; the cars are shown t
hours after noon. We know that and that .
Using s^2 = x^2 + y^2 , we get
.
At 1 P.M., x = 30, y = 40, and s = 50.
(B) (from Question 82) is zero when y = x. Note that x = 90 − 60t
and y = 40t.
