Barrons AP Calculus - David Bock
(D) The graph of f being concave downward implies that f ′′ < 0, which implies that f ′ is decreasing. ...
(D) Speed is the magnitude of velocity; at t = 3, speed = 10 ft/sec. ...
(D) Speed increases from 0 at t = 2 to 10 at t = 3; it is constant or decreasing elsewhere. ...
(E) Acceleration is positive when the velocity increases. ...
(D) Acceleration is undefined when velocity is not differentiable. Here that occurs at t = 1, 2, 3. ...
(A) Acceleration is the derivative of velocity. Since the velocity is linear, its derivative is its slope. ...
(C) Positive velocity implies motion to the right (t < 2); negative velocity (t > 2) implies motion to the left. ...
(B) The average rate of change of velocity is ...
(E) The slope of y = x^3 is 3x^2. It is equal to 3 when x = ±1. At x = 1, the equation of the tangent is y − 1 = 3(x − 1) or y ...
(C) Let the tangent to the parabola from (3, 5) meet the curve at (x 1 , y 1 ). Its equation is y − 5 = 2 x 1 (x − 3). Since th ...
66. (E) ...
(D) The graph of f ′(x) = x sin x − cos x is drawn here in the window [0,4] × [−3,3]: A local maximum exists at x = 0, where f ...
(C) f ′′ changes sign when f ′ changes from increasing to decreasing (or vice versa). Again, use your calculator to approximate ...
(E) Eliminating t yields the equation ...
70. (B) ...
(A) Since We note that, as t increases through 2, the sign of |v| ′ changes from negative to positive, assuring a minimum of |v ...
(C) The direction of a is the acceleration is always directed downward. Its magnitude, is 2 for all t. ...
(D) Using the notations vx, vy, ax, and ay, we are given that where k is a constant. Then ...
74. (E) ...
(B) The rate of change of the distance from the origin with respect to time is given by ...
«
41
42
43
44
45
46
47
48
49
50
»
Free download pdf