Answers and Explanations 281
Answers
401–500
429.
3.987
To estimate the value, you can find a linearization by using f
 
(x) = x
2/3
and a = 8 and
then substitute 7.96 into the linearization.
Find a point on the line by entering the value of a in the function. For the given value
of a, the corresponding y value is
f ( )
8
8
8
4
2 3
1 3 2
=
=
=
( )
Next, find the derivative of the function to get the slope of the line:
′
′
f x
x
x
f
( )
( )
( )
=
=
=
=
=
−
2
3
2
3
8
2
3 8
2
3 2
1
3
1 3
3
3
Using the point-slope formula with the slope m = 1
3
and the point (8, 4) gives you
y y m x x
y
x
y
x
y
x
− =
−
− =
−
=
− +
=
+
1
1
4 1
3
8
1
3
8
3
4
1
3
4
3
(
)
(
)
Replacing y with L(x) gives you the linearization L x
x
( ) = +
1
3
4
3
.
Finally, substitute in the value x = 7.96 to find the estimate:
L( . )
.
.
7 96
1
3
7 96 4
3
3 987
= (
) + ≈
430.
10 1
.
To estimate the value, you can find a linearization by using f x
x x
( ) =
=
1 2 and a = 100
and then substitute 102 into the linearization.