Barrons AP Calculus
(b) feet TP = 5280(5 − u) Costs (dollars): 2[5280(5 − u)] If C(u) is the total cost, We now minimize C(u): . ...
If f ′(c) does not exist, check the signs of f ′ as x increases through c: plus-to- minus yields a local ...
Figure N4–12 Point x = Behavior of f Behavior of f ′ c (^1) f (c 1 ) is a local max f ′ (c 1 ) = 0; ...
graph of f changes concavity from up to down decreasing; f ′(c 4 ) is a local maximum c (^5) f (c 5 ) is a ...
= 2. We use the information obtained to sketch a possible graph of f, shown in Figure N4–14. Note that ...
(a) (b) (c) (d) (e) (a) (b) (c) (d) A particle moves along a horizontal line such that its position s ...
(e) P’s motion can be indicated as shown in Figure N4–15. P moves to the right if t < 1, reverses its ...
(a) (b) (c) (d) (e) Thus s increases if t > 3. v increases if t < 0 or t > 2. Since v and a have ...
BC ONLY If a point P moves along a curve defined parametrically by P(t) = (x(t), y(t)), where t repr ...
Velocity vector The velocity vector is the derivative of the vector function (the position vector): Al ...
BC ONLY ...
(a) (b) (c) (d) (e) (a) (b) Acceleration vector The acceleration vector a is , and can be obtained by ...
(c) v = −3 sin t, 2 cos t a = −3 cos t, −2 sin t = −R. The acceleration, then, is always directed to ...
(d) (e) BC ONLY The curve, and v and a at t 1 and t 2 , are sketched in Figure N4–18, below. Figure N4–18 Fo ...
applying the usual tests to sort out values of t that yield maximum or minimum speeds. Example 29 __ A p ...
and ...
BC ONLY vx^2 + vy^2 = 10, (2) vx^2 + (2x − 1)^2 vx^2 = 10. (3) Relation (3) holds at all times; specificall ...
Figure N4–19b †Local linear approximation is also referred to as “local linearization” or even “best linea ...
(a) (b) (c) (d) Figure N4–20 where f (a) + f ′(a)(x − a) is the linear or tangent-line approximation for f (x ...
(a) (b) (c) (d) At a = 0, sin x sin (0) + cos (0)(x − 0) 0 + 1 · x x At a = 1, 2x^3 − 3x − ...
«
8
9
10
11
12
13
14
15
16
17
»
Free download pdf