Local Linearity and Linearization
AP Calculus AB · Flashcards · Recall
AP CALCULUS AB · FLASHCARDS
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QUESTION
Which function value is used in the linear approximation
L
(
x
)
=
f
(
a
)
+
f
′
(
a
)
(
x
−
a
)
L(x) = f(a) + f'(a)(x - a)
L
(
x
)
=
f
(
a
)
+
f
′
(
a
)
(
x
−
a
)
?
QUESTION
State the condition under which a function is locally linear at a point.
QUESTION
Which function approximates
f
(
x
)
f(x)
f
(
x
)
near
x
=
a
x = a
x
=
a
using local linearity?
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ANSWER
The linearization
L
(
x
)
L(x)
L
(
x
)
of
f
(
x
)
f(x)
f
(
x
)
. The best linear approximation near the given point.
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