–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