Local Linearity and Linearization
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Determine the linear approximation of
f
(
x
)
=
ln
(
x
)
f(x) = \text{ln}(x)
f
(
x
)
=
ln
(
x
)
at
x
=
e
x = e
x
=
e
for
x
=
e
+
0.1
x = e+0.1
x
=
e
+
0.1
.
QUESTION
Which function value does
f
(
a
)
f(a)
f
(
a
)
represent in the linear approximation formula?
QUESTION
Evaluate
L
(
x
)
L(x)
L
(
x
)
for
f
(
x
)
=
cos
(
x
)
f(x) = \text{cos}(x)
f
(
x
)
=
cos
(
x
)
at
x
=
π
2
x = \frac{\text{π}}{2}
x
=
2
π
using
x
=
π
2
+
0.1
x = \frac{\text{π}}{2} + 0.1
x
=
2
π
+
0.1
.
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ANSWER
L
(
x
)
=
0
−
0.1
=
−
0.1
L(x) = 0 - 0.1 = -0.1
L
(
x
)
=
0
−
0.1
=
−
0.1
.
f
(
π
2
)
=
0
f(\frac{\pi}{2}) = 0
f
(
2
π
)
=
0
,
f
′
(
π
2
)
=
−
1
f'(\frac{\pi}{2}) = -1
f
′
(
2
π
)
=
−
1
, so slope is negative.
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