Math 2413
Homework Set 6
10 Points
Implicit Differentiation
For problems 1 & 2 find
y
¢
.
1.
( )
2
63
co
s
21
x
yyx
=+
2.
( )
3
2
25
3
x
y
yx


=+
3.
Find the equation of the tangent line to
3
4
15
xy
y
=
e
at (0, 2).
Related Rates
In order to receive any credit for problems 4 – 7 you MUST use Calculus techniques to find the answer.
Any decimal work should include at least 4 decimal places.
4.
A snowball in the shape of a sphere is melting and losing volume at a rate of 3 cm
3
/sec.
How fast is
the radius of the snowball decreasing when the surface area of the snowball is 35 cm
2
?
5.
A water tank is in the shape of a cone whose base radius of 20 ft and height is 50 ft and water is
entering the tank at a rate of 6 ft
3
/hr.
At what rate is the height of the water changing when the height
of the water is 12 ft.
6.
Two people start out 750 meters apart with person A directly to the west of person B.
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 Calculus, Derivative, Implicit Differentiation, Convex function

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