AP Calculus: Derivatives and Applications of derivatives, Integrals, Application of Integrals Online Test


9/2
9.07
6.2
7/2
3.1



5 feet
37 feet
21 feet
53 feet
45 feet
For the curve given by the equation g(x)= x3+x4
No extrema exist
There is minimum at x=3/4
There is maximum at x=-3/4
There is minimum at x=-3/4
There is maximum at x=3/4

None of the above
A 13ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2ft/sec how fast will the foot of the ladder be moving away from the wall when the top is 5ft above the ground?
3 ft/sec
4 ft/sec
7 ft/sec


The line 2x +3y = a is tangent to the graph of f(x)=bx2 at the point where x = 3. Then the values of a and b are respectively given by
-1/9, 3
3, 1/9
3, -1/9
1/9, 3
-1/9, -3

the curve has a turn at x=6
(6, 0.479) is local minimum point for f(x)
x-axis is horizontal asymptote for the curve
There are no vertical tangents for the curve.
Domain of f(x) is [0, ()
A railroad track and a road cross at right angles. An observer stands on the road 140 meters south of the crossing and watches a train traveling at 80 meters per second. At how many meters per second is the train moving away from the observer 6 seconds after it passes through the intersection?
59.60
76.8
79.20
62.00
47.40

1
2

18
15
16
11
35

24
41
29
45
9


17.42
15.32
13.21
15.64
19.23

1/3
8/3
1
0
2/3


Description:

This test contains twenty questions on 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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