# AP Calculus AB Test : Derivatives

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Given that g’(x)=12(x2-4)(x+1), for the function g(x) in the interval [1, 3],____
The value g(3) is maximum
The value g(3) is minimum
The value g(2) is maximum
The value g(2) is minimum
None of the above
Find two positive numbers that satisfy given requirements: The sum of first number squared and second is 27 and the product is maximum.
5 and 2
3 and 18
1 and 26
4 and 11
2 and 23
The line x +2y = 2 is tangent to the graph of f(x)=ax+bx2 at the point (-2, 2).Then the values of a and b are respectively given by
-3/2, 1/4
3/2, 1/4
-3/2, -1/4
3/2, 4
-3, -1/4
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the curve has a turn at x=2
x-axis is horizontal asymptote for the curve
Domain of f(x) is (-(,()
There are no vertical tangents for the curve.
The line x=2 is one of the vertical asymptotes
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24
44
18
28
12
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2
-1
9
4
0
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12
14
24
10
8
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23/12
3/4
6
13/24
3
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8
5
1
6
3
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ƒ is continuous at x = a
ƒ has a relative maximum at x = a
x = a is in the domain of ƒ
Let ƒ be the function given by ƒ(x) = 3e2x and let g be the function given by g(x) = 6x3. At what value of x do the graphs of ƒ and g have parallel tangent lines?
–0.701
–0.567
–0.391
–0.302
–0.258
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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