Estimating Derivatives of a Function
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Which difference quotient is more accurate: forward or symmetric?
QUESTION
Identify the error:
f
′
(
a
)
≈
f
(
a
+
h
)
+
f
(
a
−
h
)
2
h
f'(a) \approx \frac{f(a+h) + f(a-h)}{2h}
f
′
(
a
)
≈
2
h
f
(
a
+
h
)
+
f
(
a
−
h
)
QUESTION
Estimate
f
′
(
3
)
f'(3)
f
′
(
3
)
for
f
(
x
)
=
sin
x
f(x) = \sin x
f
(
x
)
=
sin
x
using
h
=
0.01
h = 0.01
h
=
0.01
and the forward difference quotient.
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ANSWER
-0.9895. Forward formula:
sin
(
3.01
)
−
sin
(
3
)
0.01
≈
−
0.9895
\frac{\sin(3.01) - \sin(3)}{0.01} \approx -0.9895
0.01
s
i
n
(
3.01
)
−
s
i
n
(
3
)
≈
−
0.9895
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