Math homework
tallpn
assignment4.2.pdf
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.
