# AP Calculus AB: Applications of Derivatives and Integrals online Test


x<2
0 x>-1
x>3

-2
11/9
11/18
11/3
33/18

-14
-2
12
16
None of these
The point on the curve x2-2y = 0 that is the nearest point ( 0,-4) occurs has the y coordinate equal to
½
0
-1/2
-1
None of the above

-tan x
-cot x-1
Cot x-1
Tan x
Csc x

-1
-9/2
9/2
1
None of the above

1
If f(x) = x3 + 3x2 +4x +5 and g(x) = sinx, then g’(f(0)) =
4 cos4
0
1
4cos5
5

- sin2x
1 –2cos2x
Cos2 x
1-sin2x
2-4sin2x
If the line 3x - 4y = 0 is tangent in the first quadrant to the curve y = x3 + k , then k is
½
¼
0
-1/8
-1/2
If f (x) = 2x3 + Ax2 + Bx - 5 and if f (2) = 3 and f (-2) = -37, what is the value of A+ B?
-6
-3
-1
2
It cannot be determined from the information given.
If f’’(x) – f’(x) -6f(x) = 0,f’(0)= -4 and f(0) = -2 then f(1) =
e3+e-2
0
e3
2e-2

4e4(x-1)
3 + x3
4 -xe4(x-1)
2x2 +2
If cos(xy) = x , then dy /dx =


-2
3/25
25/3
-1/2
0

x – 4y = 0
x – y = 0
x = 0
y = 0
x+4y=0
A region in the plane is bounded by the graph of y = 1/x the x-axis the line x= m, and the line x = 3m, m>0. The area of this region
Is independent of m
Increases as the m increases
Decreases as the m increases
Decreases as m increases when m<1/3; increases as m increases when m >1/3
increases as m increases when m<1/3; decreases as m increases when m >1/3

2
2.03
2.096
1.94
1.24

1
Description:

This test contains twenty questions on Continuity, Derivatives and Applications of derivatives, Integrals, Application of Integrals. 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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