Study Guide for Third Test, MA 139 Has more questions than the test
SHOW YOUR WORK. If work is needed, there is no credit without work shown.
Use EXACT answers unless it is a word problem.
Write your answers on the lines provided. Failure to do so loses points.
Increasing f ′ > 0 Concavity f ′′
Decreasing f ′ < 0 Inflection pt where f ′′ changes if f defined
Rel min or max where f ′ changes Rel min or max f ′ 0; sign of f ′′
Abs min or max ** only on change of f′ if domain all reals
(unless equal values of y at more than one place)
** OR if finite domain, then lowest and highest y
(check endpoints and critical points)
loga
y
xy a x=⇔ = NMNM aa
=
⇔
=
loglog
logaMN = logaM + logaN NM
N
M
aaa logloglog −= a
x
x
aln
ln
log =
logaMr = rlogaM a
M
aMlog
=
loga
M
aM=
A=P(1 + rt)
mt
m
r
PA
+= 1
rt
PeA =
mt
m
r
AP
−
+= 1
()
u
dx
d
ee
dx
duu = 0
1
ln ≠= xif
x
x
dx
d 0
1
ln >
′
== uif
u
u
u
dx
d
u
u
dx
d
kt
oeQtQ =)( kt
B
e
A
tQ −
+
=1
)(
Old Stuff:
gfgffg ′
+
′
=
′
)( 2
g
gfgf
g
f′
−
′
=
′
1. Find the following (some may not exist) for the functions below:
A. f(x) = 2x3 -6x2 + 6x + 2 B. x
xf +
=1
2
)( C. f(x) = 2x4 – 36x2 + 27
a. where is it increasing? b. where is it decreasing? c. relative minimum(s)?
d. relative maximum(s)? e. concave upward? f. concave downward?
g. inflection points?
2. Find the derivative (A) f(x) = 2x2e-6x (B) f(x) = ln (6x3 + 2x2 -3) (C) f(x) = x ln x
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