Estimating Derivatives of a Function
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Estimate
f
′
(
x
)
f'(x)
f
′
(
x
)
at
x
=
11
x = 11
x
=
11
using
f
(
10.9
)
=
22.2
f(10.9) = 22.2
f
(
10.9
)
=
22.2
and
f
(
11.1
)
=
22.8
f(11.1) = 22.8
f
(
11.1
)
=
22.8
.
QUESTION
Estimate
f
′
(
2
)
f'(2)
f
′
(
2
)
if
f
(
1.9
)
=
3.5
f(1.9) = 3.5
f
(
1.9
)
=
3.5
and
f
(
2.1
)
=
4.1
f(2.1) = 4.1
f
(
2.1
)
=
4.1
.
QUESTION
Estimate
f
′
(
x
)
f'(x)
f
′
(
x
)
at
x
=
1
x = 1
x
=
1
using
f
(
0.9
)
=
2.6
f(0.9) = 2.6
f
(
0.9
)
=
2.6
and
f
(
1.1
)
=
2.8
f(1.1) = 2.8
f
(
1.1
)
=
2.8
.
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ANSWER
2.8
−
2.6
1.1
−
0.9
=
1.0
\frac{2.8 - 2.6}{1.1 - 0.9} = 1.0
1.1
−
0.9
2.8
−
2.6
=
1.0
. Apply the difference quotient formula to estimate the derivative.
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