Review – No Calculator
Worksheet 119
NO CALCULATOR FOR PROBLEMS 1-13!
20x 2  13x  5

x
5  4x 3
1. lim
2. lim
h0
ln 2  h  ln 2
=
h
3. If y  e x , find y"0 .
2
The table shown is for Questions 4 and 5. The differentiable functions f and g have the values shown.
4. Find the average rate of change of the function f on [1,4].
5. If h  x   g  f  x   , find h '  3.
6. The derivative of a function f is given for all x by f ' x   x 2 x 1 x  4  . The set of x for which f is a relative
maximum is at which x value(s)?
3
2
7. At which point on the graph of y  f x  shown above is f ' x   0 and f "x   0 ?
8. If the radius r of a sphere is increasing at a constant rate, then the rate of increase of the volume of the sphere is
(A) constant
(B) increasing
(C) decreasing
(D) increasing for r  1 and decreasing for r  1
(E) decreasing for r  1 and increasing for r  1
For questions 9, 10, and 11, the graph shows the velocity of an object moving along a line, for 0  t  9 .
9. When does the object attain its maximum acceleration?
10. When is the object farthest from the starting point?
11. At t  8 , the object was at position x  10 . Find x 5 .

12.
13.


2
sin 3  cos  d 
4
1
0
ex
3  e 
x 2
dx 
14. Consider the curve defined by the equation: y  cos y  x 1 for 0  y  2 .
dy
in terms of y .
(a) Find
dx
(b) Write an equation for each vertical tangent to the curve.
d2y
(c) Find 2 in terms of y.
dx
Answers:
1) 0
1
2
8
9)  t  9
3) -2
2)
8) B
14) b. x 

2
1
14) c.
4
3
11) 13
5) 1
6) None
7) A
4)
10) 6
12)
cos y
1 sin y 3
2007 #4
3
16
13)
e 1
2 3  e
14) a.
1
1 sin y