Local Linearity and Linearization
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
Card 1
of 23
0 got it
0 to review
Current
Got it
Still learning
Not seen
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
Which function approximates
f
(
x
)
f(x)
f
(
x
)
near
x
=
a
x = a
x
=
a
using local linearity?
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
.
Tap to flip before you grade
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
.
Swipe → got it · swipe ← still learning
Got it
Still learning
Flip Card
Previous card
Next card