MA 141 Turn in Homework Quiz 4.2 Pitts Name ____________________________ 1. (#34) Let f(x) = 3x4 – 6x3 + x – 8. Determine where the function is concave upward and where it is concave downward. Show your calculus. Show your sign graph. In interval notation: concave up ______________________ concave down _______________________ 2. (#38) Let ( ) 2g x x  . Determine where the function is concave upward and where it is concave downward. Show your calculus. 3. Let 2 ( ) 3 x f x x    . Determine where the function is concave upward and where it is concave downward. Show your calculus. Show your sign graph. In interval notation: concave up ______________________ concave down _______________________ 4. Consider the function 4 3 ( ) 4 5f x x x   . Show your calculus. a.) Using the first derivative, find all critical values for potential relative extrema. b.) Use the second derivative test to find all relative maximum and minimum points. c.) Determine if there are any points of inflection. Show your calculus! Show your sign graph. 5. (# 60) Determine the intervals where the function is concave up or down, and also determine if there are any points of inflection for the function 3 ( ) 2f x x   . 6. (# 72) Using the second derivative test, determine if there are any relative extrema for the function 2 2 ( )g x x x   . 7. (#74) Consider function 2 1 ( ) 1 g x x   . Find any relative extrema. Use the first or second derivative test to justify whether it is a maximum or a minimum. You do not need to simplify the second derivative. 8. (#78) Sketch the graph of a function (2) 2f  , (0) 1f  , '(2) 0f  , '( ) 0f x  for x < 2, '( ) 0f x  for 2x  , ''( ) 0f x  for x < 2, and "( ) 0f x  for x > 2. 9. In a study conducted in 2003, it was projected that worldwide PC shipments (in millions) through 2005 will be given by 3 2 ( ) 0.75 1.5 8.25 133 (0 t 4)n t t t t      where t is measured in years, with t = 0 corresponding to 2001. Make sure to show sign graphs were necessary. Determine the intervals where N is concave upward and where it is concave downward. Also find an inflection point(s) and interpret the results. MA 141 Homework 4.1 Pitts SHOW YOUR WORK! Name _______________________ 1. (See # 20) Find the interval(s) where the function 3 ( ) 3 4f x x x   is increasing and the interval(s) where it is decreasing. Show your calculus to justify your answer. Show your sign graph clearly In interval notation: increasing over ______________________ decreasing over ______________________ 2. (See # 28) Find the interval(s) where the function 2 2 ( ) 1 t g t t   is increasing and the interval(s) where it is decreasing. Show your calculus to justify your answer. Show your sign graph clea ...

1. MA 141 Turn in Homework Quiz 4.2
Pitts Name ____________________________
1. (#34) Let f(x) = 3x4 – 6x3 + x – 8. Determine where the
function is concave upward and where it is concave
downward. Show your calculus. Show your sign graph.
In interval notation: concave up ______________________
concave down _______________________
concave upward and where it is concave downward.
Show your calculus.

2. 3. Let
2
( )
3
x
f x
x
. Determine where the function is concave upward and where it
is concave downward. Show
your calculus. Show your sign graph.
In interval notation: concave up ______________________
concave down _______________________

3. 4. Consider the function
4 3
a.) Using the first derivative, find all critical values for
potential relative extrema.
b.) Use the second derivative test to find all relative maximum
and minimum points.
c.) Determine if there are any points of inflection. Show your
calculus! Show your sign graph.
5. (# 60) Determine the intervals where the function is concave
up or down, and also determine if there are any
points of inflection for the function
3

4. ( ) 2f x
x
6. (# 72) Using the second derivative test, determine if there
are any relative extrema for the function
2 2
( )g x x
x
.
7. (#74) Consider function
2
1
( )
1
g x

5. x
. Find any relative extrema. Use the first or second derivative
test to
justify whether it is a maximum or a minimum. You do not need
to simplify the second derivative.
8. (#78
9. In a study conducted in 2003, it was projected that
worldwide PC shipments (in millions) through 2005 will
be given by

6. 3 2
measured in years, with t = 0
corresponding to 2001. Make sure to show sign graphs were
necessary. Determine the intervals where N is
concave upward and where it is concave downward. Also find
an inflection point(s) and interpret the results.
MA 141 Homework 4.1
Pitts SHOW YOUR WORK! Name
_______________________
1. (See # 20) Find the interval(s) where the function
3
where it is decreasing. Show your calculus to justify your
answer. Show your sign graph clearly

7. In interval notation: increasing over ______________________
decreasing over ______________________
2. (See # 28) Find the interval(s) where the function
2
2
( )
1
t
g t
t
is increasing and the interval(s) where it
is decreasing. Show your calculus to justify your answer. Show
your sign graph clearly

8. In interval notation: increasing over ______________________
decreasing over ______________________
3. (See # 36) Showing your calculus, find the interval(s) where
the function
2
( )
1
x
g x
x
is increasing and the
interval(s) where it is decreasing. Show your sign graph
clearly.
In interval notation: increasing over ______________________

9. decreasing over ______________________
4. (See # 60) Showing your calculus, find the relative maxima
and relative minima, if any, of the
function
5 3
5. (See # 68) Showing your calculus, find the relative maxima
and relative minima, if any, of the
function
2
( )
1
x
g x
x

10. . Justify your answer.
6. (See 4.1 # 72) The Mexican subsidiary of ThermoMaster
manufactures an indoor-outdoor thermometer.
Management estimates that the profit (in dollars) realizable by
the company for manufacture and sale of x units of
thermometers each week is
2
( )
the interval(s) where
the profit function P is increasing and the interval(s) where P is
decreasing?

11. 7. (See 4.1 # 78) The average cost (in dollars) incurred by
Lincoln Records each week in pressing x compact discs
is given by
2000
( ) 0.0001 2 (0 6000)C x x x
x
decreasing over the interval (0, 6000).