These are problems that cover material which will be on Friday’s test. Note that
interpretation of the derivative was on a previous test in 2006. Topics from Ch. 6
will be given on a Part II Test on Thursday, 11/13.
Math 129 Name___________________________
Show all work in order to receive credit.
1. Use l’Hopital’s rule, if appropriate, to find the following limits: (10 pts)
a)
)(lim
2x
x
ex
b)
3ln
8
lim
2
3
2
x
x
x
2. For the function f(x) =
3 2
3 4x x
. Use the methods of calculus to answer the following. (12 pts)
Construct charts for the first and second derivative and use them to answer the following.
f has critical points at __________
f increases __________________ f decreases _____________________
f has local maximum(a) of __________ at __________
f has local minimum(a) of __________ at __________
f is concave up on _____________ f is concave down on ______________
f has inflection point(s) of ________________
Find other key points and sketch the graph.
3. For the function
( ) x
g x xe
. Use the methods of calculus to answer the following. (12 pts)
Construct charts for the first and second derivative and use them to answer the following.
g has critical points at __________
g increases __________________ g decreases _____________________
g has local maximum(a) of __________ at __________
g has local minimum(a) of __________ at __________
g is concave up on _____________ g is concave down on ______________
g has inflection point(s) of ________________
Find other key points and sketch the graph.
4. Consider the family of functions of the form f(x) = ex - kx , for k > 0. (10 pts)
