Barrons AP Calculus - David Bock
74. (E) ...
(B) The rate of change of the distance from the origin with respect to time is given by ...
(B) In parametric form, x = r cos = 6 cos 2 cos ; hence: ...
(B) A local minimum exists where f changes from decreasing (f ′ < 0) to increasing (f ′ > 0). Note that f has local maxim ...
(D) See Answer 68. ...
(D) At x = a, f ′ changes from increasing (f ′′ > 0) to decreasing (f ′′ < 0). Thus f changes from concave upward to conc ...
(C) We know that ...
(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 Using s^2 = x^2 + y ...
(B) (from Question 82) is zero when Note that x = 90 − 60t and y = 40t. ...
(B) Maximum acceleration occurs when the derivative (slope) of velocity is greatest. ...
(B) The object changes direction only when velocity changes sign. Velocity changes sign from negative to positive at t = 5. ...
(D) From the graph, f ′(2) = 3, and we are told the line passes through (2,10). We therefore have f (x) 10 + 3(x − 2) = 3x + 4. ...
(C) At x = 1 and 3, f ′(x) = 0; therefore f has horizontal tangents. For x < 1, f ′ > 0; therefore f is increasing. For ...
(C) Note that at Q, R, and T. At Q, at T, ...
(D) Only at S does the graph both rise and change concavity. ...
(E) Only at T is the tangent horizontal and the curve concave down. ...
(C) Since f ′(6) = 4, the equation of the tangent at (6, 30) is y − 30 = 4(x − 6). Therefore f (x) 4 x + 6 and f (6.02) 30.08. ...
92. (C) ...
Answers Explained All the references in parentheses below are to the basic integration formulas. In general, if u is a function ...
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