For problems 1 
3 use the graph of the function, ,
estimate the value of for the given values of a.
1. (a) (b)
2. (a) (b)
3. (a) (b)
For problems 4 6 sketch the graph of a function that
satisfies the given conditions.
4. ,
,
,
5. ,
,
,
6. ,
,
,
,
,
For problems 7 9 the graph of a function, ,
is given. Use this to sketch the graph
of the derivative, .
7.
8.
9.
10. Answer the following questions about the function .
(a) Is the function increasing or
decreasing at ?
(b) Is the function increasing or
decreasing at ?
(c) Does the function ever stop
changing? If yes, at what value(s) of z does the
function
stop changing?
11. What is the equation of the tangent line to at .
12. The position of an object at any time t is given by .
(a) Determine the velocity of the
object at any time t.
(b) Is the object moving to the right
or left at ?
(c) Is the object moving to the right
or left at ?
(d) Does the object ever stop
moving? If so, at what time(s) does the
object stop
moving?
13. Does the function ever stop changing? If yes, at what value(s)
of w does the function stop changing?
14. Suppose that the volume of air in a balloon for is given by .
(a) Is the volume of air increasing or
decreasing at ?
(b) Is the volume of air increasing or
decreasing at ?
(c) Does the volume of air ever stop
changing? If yes, at what times(s) does
the
volume stop changing?
15. What is the equation of the tangent line to at ?
16. Answer the following questions about the function .
(a) Is the function increasing or
decreasing at ?
(b) Is the function increasing or
decreasing at ?
(c) Does the function ever stop
changing? If yes, at what value(s) of x does the
function
stop changing?
17. Determine if the function increasing or decreasing at the given points.
(a)
(b)
(c)
18. Suppose that the volume of water in a tank for is given by .
(a) Is the volume of water increasing
or decreasing at ?
(b) Is the volume of water increasing
or decreasing at ?
(c) Does the volume of water ever stop
changing? If so, at what times(s) does
the
volume stop
changing?
19. What is the equation of the tangent line to at ?
20. The position of an object at any time t is given by .
(a) Determine the velocity of the
object at any time t.
(b) Does the object ever stop
moving? If so, at what time(s) does the
object stop
moving?
21. Does the function ever stop changing? If yes, at what value(s)
of t does the function stop changing?