Name _________________________________
3020 Function Analysis A
1)
Period ____________________
Use the FIRST DERIVATIVE TEST to find the intervals where the function is
increasing and where it is decreasing. Justify your answer.
f ( x)  3 x 3  2 x
2)
Use the FIRST DERIVATIVE TEST to find the function’s local extrema.
Justify your answer.
f ( x) 
3)
x 1
x2  2 x  2
Use the given BRICK WALL to find and justify
a) the intervals where the function is increasing and decreasing, and
b) the maximum and minimum locations.
f (x) is a continuous function with critical numbers at -3 , 0 , 1, 4. The sign of the
derivative on each interval is shown.
f ‘ (x)
f (x)
+
-
-
+
+
4)
Create the BRICK WALL to find and justify
a) the intervals where the function is increasing and decreasing, and
b) the maximum and minimum locations and values.
f ( x)  x 3  3 x 2  3 x  2
5)
Use the FIRST DERIVATIVE TEST to find (a) where the function is increasing and
decreasing , and (b) the function’s local extrema. Justify your answer.
15
 1 2 1
 x  x 
y 4
2
4
3
2

x

6
x

8

6)
x 1
x 1
Coughing forces the trachea (windpipe) to contract, which affects the velocity v of the
air passing through the trachea. The velocity of the air during coughing is
v  k ( R  r )r 2
0r R
where k is a constant, R is the normal radius of the
trachea, and r is the radius during coughing. What radius will produce the maximum air
velocity