Name:
Due Date:
PROBLEM SET #1
Block:
All work must be shown to receive credit for all questions with an asterisk*
If you cannot think of work to show, then explain why your chose a particular answer.
You may work together but everyone turns in his or her own packet.
I will answer questions but not on the due date.
Part I: Non-Calculator
3
 x , x  0
_____1) * Let f ( x) be defined by f ( x)   2
. Then f (0) 
 x , x  0
a) 0
b) 1
c) 2
d) 6
e) DNE
_____2) Given that f ( x) is continuous for all real numbers,
x
f(x)
0
1
1
-1
2
3
3
5
4
2
Which of the following statements is necessarily true?
a)
b)
c)
d)
e)
There is some c in the interval (0, 2) such that
There is come c in the interval (1, 2) such that
There is some c in the interval (2, 4) such that
There is some c in the interval (0, 3) such that
There is some c in the interval (0, 4) such that
f (c )  4
f ( c )  5
f (c )  6
f (c )  2
f ( c )  3
_____3) The graph of the function f is shown in the figure. For what values of x, -2 < x < 4, is f not
differentiable?
Graph of f
a)
b)
c)
d)
e)
0 only
0 and 2 only
2 and 3 only
0 and 3 only
0, 1, and 3 only
_____4)* The y – intercept of the tangent line to the curve y  x  3 at the point 1, 2  is
a)
1
4
b)
1
2
c)
3
4
d)
5
4
AP Calculus AB
e)
7
4
_____5)* The graph of the a function f is shown in the box. Which of the following statements
about f is false? Explain why your chose your answer.
a) f has a relative minimum at x = a.
b) lim f ( x)  lim f ( x)
x a
x a
c) lim f ( x)  f (a )
a
xa
d)
e)
f (a)  0
f ( a )  0


cos   h 
2

_____6)* lim
h 0
h
a) 1
b) 0
c) -1
d)

2
e) DNE
_____7)* The maximum value of the function f ( x)  x 4  4 x3  6 on the closed interval [1, 4] is
a) 1
b) 0
c) 3
d) 6
e) 4
 
_____8) * If f ( x)  cos x sin 3x, then f    
6
a)
1
2
b) 
____9)* The curve y 
a)  3, 
3
2
c) 0
d) 1
e) 
1 x
is concave up on which interval?
x 3
b) 1,3
c) 1, 
d )  ,1
AP Calculus AB
e)  ,3
1
2
____10) If f ( x ) exists on the closed interval  a, b then it follows that
a)
f ( x ) is constant on  a, b
b) there exists a number c   a, b  , such that f (c)  0
c) the function has a maximum value on the open interval  a, b 
d) the function has a minimum value on the open interval  a, b 
e) the mean value theorem applies
dy

dx
____11)* If y  sin3 1  2 x  then
a) 3sin 2 1  2 x 
b)  2 cos3 1  2 x 
d )  6sin 2 1  2 x  cos 1  2 x 
e)  6 cos 2 1  2 x 
c)  6sin 2 1  2 x 
____12)* The equation of the tangent line to the curve xy  x  y  2 at the point where x  0 is
1
x2
2
e) y  2  x
a) y   x
b) y 
d) y  2
c) y  x  2
____13)* The set for which the curve of y  1  6 x 2  x 4 has inflection points is
a) 0


b)  3, 3
c) 1
d ) 1,1
e) None of these
____14)* If a particle’s motion along a straight line is given by s  t 3  6t 2  9t  2, then s is increasing
on which intervals?
a) 1,3
b)  1,3
c)  ,  
d )  ,3  3,  
AP Calculus AB
e)  ,1  3,  
Part II: Free Response - Calculator Active
15) * Let h be a function defined for all x  0 such that h(4)  3 and the derivative of h is
given by h( x) 
x2  2
for all x  0 .
x
a) Find all values of x for which the graph of h has a horizontal tangent, and determine whether h
has a local maximum, a local minimum, or neither at each of these values. Justify your answers.
b) On what intervals, if any, is the graph of h concave up? Justify your answer.
c) Write an equation for the line tangent to the graph of h at x  4 .
d) Does the line tangent to the graph of h at x  4 lie above or below the graph of h for x  4 . Why?
AP Calculus AB