3. (10 pts.)
(a)
Let
f
(
x
)
e
x
3
x
Show that
f
is onetoone on
using
f
′
. [A little explanation is needed!]
(b)
Suppose that a onetoone function
f
has a tangent line given by
y
= 5
x
+ 3 at the point (1,8).
Find
f
1
(8) and (
f
1
)
′
(8).
f
1
(8)
(
f
1
)
(8)
______________________________________________________________________
4. (10 pts.)
Write down each of the following derivatives. [2 pts/part.]
(a)
d
[tan
1
]
dx
(
x
)
(b)
d
[sin
1
]
dx
(
x
)
(c)
d
[
csc
1
]
dx
(
x
)
(d)
d
[cos
1
]
dx
(
x
)
(e)
d
[cot
1
]
dx
(
x
)
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______________________________________________________________________
5. (10 pts.)
Fill in the blanks appropriately.
[DEFINITIONS!!!]
(a)
A function
f
has a relative maximum at
x
0
if there is an open interval
containing
x
0
on which
for each
x
in both the
interval and the domain of
f
.
(b)
A function
f
is concave down on an interval (
a
,
b
) if the derivative
of
f
is
on (
a
,
b
).
(c)
A function
f
is concave up on an interval (
a
,
b
) if the derivative
of
f
is
on (
a
,
b
).
(d)
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 Fall '08
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 Calculus, Derivative, Differential Calculus, Convex function, Stationary point

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