AP Calculus AB Test : Derivatives

Given that g’(x)=60(x-4)(x2+1)(x-1), for the function g(x) in the interval [0, 5],____
The value g(4) is maximum
The value g(1) is minimum
The value g(5) is maximum
The value g(0) is minimum
None of the above

The line x +3y = 5 is tangent to the graph of f(x)=ax2 +bx at the point (-1, 2). Then the values of a and b are respectively given by
-5/3, -11/3
-5/3, 11/3
5/3, -11/3
5/3, 11/3
None of the above

the curve has two turns
x-axis is horizontal asymptote for the curve
Domain of f(x) is (-(,()
There are no vertical tangents for the curve.
The line x=-3 is one of the vertical asymptotes



The function f given by f(x) = x3 –12x + 24 is
increasing for x < –2, decreasing for –2 < x< 2, increasing for x > 2
decreasing for x < 0, increasing for x > 0
increasing for all x
decreasing for all x
decreasing for x < –2, increasing for –2 < x < 2, decreasing fro x > 2

ln 6


If a function is continuous for all x and if f has a relative maximum at (-3, 2) and a relative minimum at (5, 1) which of the following statements must be true?
The graph of f has a horizontal asymptote
The graph of f has a point of inflection somewhere between x = -3 and x =5
The graph of f does not intersect the axes.
The graph of f has a horizontal tangent line at x = 3

5 and 8
10 and 15
15 and 24
2 and 12
8 and 16

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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