# AP Calculus AB: Limits and Derivatives online Test


–6
–3
2
6
8

–5
5/3
1
3/4
nonexistent

If f(x) = x1/3 ( x -2)2/3 for all x then the domain of f’ is
{x| x ? 0}
{x |x > 0}
{x| 0 = x = 2}
{x| x ? 0 and x ? 2}
{x| x is a real number}

0
Non-existent
1
2
-1

f is continuous and differentiable at every point
f is continuous at every point but is not differentiable
f is differentiable at every point except at x=0
f is differentiable only at the origin
f is neither continuous and nor differentiable

Discontinuous at x=0
Not differentiable x=0
Differentiable at x=2/3
Continuous but not differentiable at x=-2/3
Continuous but not differentiable at x=1

4
6
7
1/3
2/3


1
2

–2
4
1
3
-4

3
e
How many critical points does the function f(x) = (x – 2)5(x +4)4 have?
One
Two
Three
Five
Nine
The acceleration a of a body moving in a straight line is given in terms of time t by a = 8 - 6t. If the velocity of the body is 25 at t =1 and if s(t) is the distance of the body from the origin at time t, what is s(4) - s(2)?
20
24
28
32
42
The function f given by f(x) = x5 + 14x – 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

g is discontinuous for all x
g is differentiable for all x
g is not differentiable at three values of x
Suppose that f is a function that is defined for all real numbers. Which of the following conditions assures that f has an inverse function?
The function f is periodic
The graph of f is symmetric with respect to the y-axis.
The graph of f is concave up.
The function f is a strictly increasing function.
The function f is continuous.

23x – y = -208
23x + y = -206
x – 23y = -64
x + 23y = 14
x-23y+32=0

2
nonexistent

0
1
2/3
5/3
At no value of x
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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