Math 1325
Professor Merrill
Lab 2
Name ____________________________________
Show all work Circle Answers
Due Wed., Oct 7, 2009
1. The graph of f(x) is shown as follows:
a. On what intervals is f increasing?
b. on what intervals is f decreasing?
c. At what point(s) does f has a local
minimum?
f. On what intervals is f concaves
upward?
d. At what point(s) does f has a local
maximum?
g. State the point(s) of inflection.
e. On what intervals is f concaves
downward?
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2. A particle moves according to a law of motion s  t  12t  36t , t  0 , where t is measured in seconds
and s in meters.
a. Find the velocity function v at time t.
d. Find the points of inflection.
b. Find the critical numbers.
e. When in the particle at rest?
c. Find the acceleration function a at
time t.
f. When in the particle is moving
forward and when the particle is
moving backward?
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h. Draw a graph for all three functions
s, v, and a.
g. Find the total distance traveled
during the first 8 seconds.
i. When is the particle slowing down?
j. When is the particle speeding up?
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3. A ball is thrown upward with an initial velocity of 66 ft/s.  s(t)   t2  v0 t 
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a. Find an equation of the position of the ball in terms of time t.
b. Sketch a graph of the position function.
c. Find the velocity of the ball after 3 seconds.
4. Suppose that f (x)  1  2x 1  2x  . Find f ( x) .
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5. Suppose that f (x)  2x  1 . Find f ( x) .
2x  1
6. If f (x)  ln(3x 2  x  5)4 , find f (x). Write your answer in simplest form.
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7. If f (x)  e x  x  4 , find f (x). Write your answer in simplest form.
8. If f (x)  3x(x3  4)6 , find f (x) . Write your answer in simplest form.
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9. If f (x)  (3x  3x 2 )3 (2x  x 2 )5 , find f (x) . Write your answer in simplest form.
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 2x  x 2 
10. If f (x)  
, find f (x) . Write your answer in simplest form.
 3x  x 3 
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