The Return of
More Problems
(1) Di
ff
erentiate the following functions.
(a)
y
= ln(arcsin(3
x
) + 1)
(b)
y
= sin(arctan(ln
x
+
x
))
(c)
y
=
x
2
arccos
e
x
x
2
(d)
y
=
arctan(
e
√
x
)
1 +
x
2
(e)
y
= arcsin
(
xe
arctan
x
)
(2) A rectangle is to have fixed perimeter
P
. What dimensions give maxi
mal area?
(3) An isosceles triangle has base
and height
h
. Find the maximum area
of an inscribed rectangle with one side on the base of the triangle.
(4) At which points on the curve
y
= 1 + 40
x
3

3
x
5
does the tangent line
have the largest slope?
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 Fall '06
 McAdam
 right circular cylinder, largest possible volume

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