The first question on the prelim
(4 points) Write your name and section
number on your paper.
There will be three word problems
(not counting this one)
Equation of the tangent line
1/3
1/3
Find the equation of the tangent line to
( )
at
216. Use the tangent line to estimate
(225)
Give the answer to four decimal places
f x
x
x
=
=
0
0
0
(
)
'(
)(
)
y
f x
f
x
x
x
=
+
−
1/3
2/3
2
0
0
0
1/3
1/3
( )
'( )
(1/3)
216
(
)
6
'(
)
1/(3 6 )
1/108
6
(
216)/108
9
1
(225)
6
6
6.0833
108
12
(225)
exp((1/3)ln(225))
6.0822
f x
x
f
x
x
x
f x
f
x
y
x
−
=
=
=
=
=
⋅
=
=
+
−
≈
+
=
+
=
=
=
Monkeyface prickelback
/ 4
2.5
16(1
) inches
0.01
pounds
Find
/
t
L
e
W
L
dW
dt
−
=
−
=
/ 4
2.5
1.5
/ 4
/ 4
1.5
/ 4
/ 4
1.5
/ 4
16(1
)
0.01
/
0.025
/
(16)(1/ 4)
/
0.025[16(1
)]
4
0.64(1
)
t
t
t
t
t
t
L
e
W
L
dW
dL
L
dL dt
e
dW
dt
e
e
e
e
−
−
−
−
−
−
=
−
=
=
=
=
−
=
−
dW
dW
dL
dt
dL
dt
=
⋅
Solution 2
/ 4
2.5
/ 4
2.5
/ 4
1.5
/ 4
/ 4
1.5
/ 4
16(1
) inches
0.01
pounds
Find
/
( )
0.01(16(1
))
'( )
0.01(2.5)(16(1
))
(4
)
0.64(1
)
t
t
t
t
t
t
L
e
W
L
dW
dt
W t
e
W
t
e
e
e
e
−
−
−
−
−
−
=
−
=
=
−
=
−
=
−

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*