92.131
Calculus 1
Geometry of Functions
For Questions 1-4: i) On what intervals is the function
)
(
x
f
increasing? Decreasing? ii) What are the relative
extrema? iii) On what intervals is the function
)
(
x
f
concave up?
Concave down?
iv) What are the points of
inflection?
v) What is the equation of the line tangent to the graph of
)
(
x
f
at
1
=
x
?
1)
2
4
2
1
4
1
)
(
x
x
x
f
+
=
2)
4
)
(
2
+
=
x
x
x
f
3)
x
e
x
x
f
2
3
)
(
−
=
4)
x
x
x
f
ln
)
(
4
=
5) Consider the function
x
x
x
x
f
9
3
)
(
2
3
−
−
=
.
a)
Find the intervals of increase or and decrease.
b) Find the local maximum and minimum values.
c)
Find the intervals of concavity and any points of inflection.
6)
Let
x
e
x
x
f
2
)
(
=
.
a) Determine intervals on which
f
is increasing and decreasing.
b) Determine all relative extrema of
f
.
c) Determine intervals on which
f
is concave up and concave down.
d) Determine any inflection points of
f
.
7)
Let
x
e
x
x
f
−
=
4
)
(
.
a) Determine intervals on which
f
is increasing and decreasing.
b) Determine all relative extrema of
f
.
c) Determine intervals on which
f
is concave up and concave down.
d)
Determine any inflection points of
f
.
8)
Suppose that
1
3
2
3
4
1
)
(
2
3
4
+
+
−
=
x
x
x
x
f
a)
On what intervals is the function
)
(
x
f
increasing? Decreasing?
b) On what intervals is the function
)
(
x
f
concave up?
Concave down?
c)
What are the points of inflection? (If, any.)
d)
What is the equation of the line tangent to the graph of
)
(
x
f
at
1
=
x
?

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