Another AP Calculus BC Test : Limits and continuity, derivatives of functions, series

In the xy-plane, the graph of the parametric equations x = 5t + 2 and y = 3t, for –3 ( t ( 3, is a line segment with slope
3/5
2
3
5/3
1/3

1/2
3/8
1
3/4
Non-existent
The slope of the line tangent to the curve y2 + (xy + 1)3 = 0 at (2, –1) is
3/4
-3/4
-2/3
1
-3/2
If ƒ and g are twice differentiable and if h(x) = ƒ(g(x)), then h”(x) =
ƒ"(g(x))g’(x) + ƒ’(g(x))g”(x)
ƒ"(g(x))
ƒ"(g(x))g’’(x)
ƒ"(g(x))[g”(x)]2
ƒ”(g(x))[g’(x)]2 + ƒ’(g(x))g”(x)

A particle moves on a plane curve so that at any time t > 0 its x-coordinate is t3 – t and its y-coordinate is (2t – 1)3. The acceleration vector of the particle at t = 1 is
(0, 1)
(2, 4)
(2, 8)
(6, 24)
(6, 12)
If ƒ is the function defined by ƒ(x) = 3x5 – 5x4, what are all the x-coordinates of points of inflection for the graph of ƒ?
–1
1
0 and 1
0 only
–1, 0 and 1

The acceleration of a particle moving along the x-axis at time t is given by a (t) = 4t + 1. If the velocity is 15 when t = 3 and the position is 10 when t = 6, then the position x(t) =

ƒ"(1) < ƒ(1) < ƒ’(1)
ƒ(1) < ƒ”(1) < ƒ’(1)
ƒ(1) < ƒ’(1) < ƒ”(1)
ƒ'(1) < ƒ(1) < ƒ”(1)
ƒ"(1) < ƒ’(1) < ƒ(1)

4
-4
1
-2
3
For what value of x does the function f(x) = (x +3)3(x –1)2 have relative minimum?
–3
-3/5
-5/2
1/3
1

0
-1/2
1/2
-3/5
Non-existent

6.08 only
7.8 only
7.8 and 9.2
6.08 and 17.9
5

5
0
1
2
6

-1

increasing for x < –10, decreasing for –10 < x< 2, increasing for x > 2
decreasing for x < 2, increasing for x > 2
increasing for all x
decreasing for all x
decreasing for x < –10, increasing for –10 < x < 2, decreasing for x > 2
How many critical points does the function f(x) = (x -5)3(x+2)2 have?
Nine
Five
One
Two
Three

10/3
8/3
40/3
20/3
15

1
-1/4
-2/3
1/4
-1
Description:

This test contains twenty questions on Limits and continuity of functions, derivatives and Applications of Derivatives. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. Wherever appeared, lnx represents the natural logarithm of x with base e. Sometimes, the options may not contain exact numerical value of an answer. In that case, select best approximation to the numerical value you got. After examining the form of the choices, decide the best of the choices given.

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