Fall 2009 Math 151
3
Week in Review XI
Setion 5.3
ourtesy: David J. Manuel
1. Determine where the funtion f (x) =
x3 − 3x2 + 5 is inreasing, dereasing,
(overing 5.1, 5.2, and 5.3)
2. Find
onave up, and onave down.
the
horizontal
and
vertial
asymptotes, intervals of diretion, and
intervals of onavity for
1
x2 |
Setion 5.1
3. Determine where the funtion f (x) =
x2 e−2x is inreasing, dereasing, on-
1. True or False-there exists a funtion
f suh that f (x) > 0, f ′ (x) < 0 and
f ′′ (x) > 0 for all x. If true, sketh it;
ave up, and onave down.
f (x) =
−x cos x + 6 cos x + 4x sin x, x ∈
[−π, π].
4. Find the inetion points of
2
if false, explain why not.
2. Sketh the graph of a funtion whih
satises the following:
•
•
•
•
f (2) = 1
f ′ (x) < 0
for
x<2
f (x) > 0
for
x>2
′
f (x) < 0
′′
3. Maplets:
of
a
Properties
of
Funtion/First
tive/Seond
Derivative
a
Graph
Deriva-
loated
at
http://allab.math.tamu.edu/maple/maplets
2
Setion 5.2
1. Find the absolute maximum and abso-
lute minimum of eah of the following:
√
(a)
f (x) =
(b)
2h sec ix − tan x on the interval
π
0,
4
f (x) = x2 e−x on the interval [1, 4]
ln x
f (x) =
on the interval (0, ∞)
x
()
(d)
6x − x2
2. Find the ritial values of
2
15x + 36x + 7
f (x) = ln |1−
and sketh the graph.
f (x) = 2x3 −
1