Local Linearity and Linearization
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Determine the linearization of
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
at
x
=
2
x = 2
x
=
2
.
QUESTION
What is the linear approximation for
f
(
x
)
=
sqrt
(
x
)
f(x) = \text{sqrt}(x)
f
(
x
)
=
sqrt
(
x
)
at
x
=
4
x = 4
x
=
4
?
QUESTION
State the linear approximation for
f
(
x
)
=
1
x
f(x) = \frac{1}{x}
f
(
x
)
=
x
1
at
x
=
2
x = 2
x
=
2
.
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ANSWER
L
(
x
)
=
1
2
−
1
4
(
x
−
2
)
L(x) = \frac{1}{2} - \frac{1}{4}(x - 2)
L
(
x
)
=
2
1
−
4
1
(
x
−
2
)
. Since
f
(
2
)
=
1
2
f(2) = \frac{1}{2}
f
(
2
)
=
2
1
and
f
′
(
2
)
=
−
1
4
f'(2) = -\frac{1}{4}
f
′
(
2
)
=
−
4
1
.
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