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Mathematics
Problem
Let
f
f
f
be differentiable at
x
=
a
x=a
x
=
a
, and let
h
>
0
h>0
h
>
0
be small. Which of the following expressions provides a symmetric numerical approximation of
f
′
(
a
)
f'(a)
f
′
(
a
)
? a)
f
(
a
+
h
)
−
f
(
a
−
h
)
h
\dfrac{f(a+h)-f(a-h)}{h}
h
f
(
a
+
h
)
−
f
(
a
−
h
)
b)
f
(
a
+
h
)
−
2
f
(
a
)
+
f
(
a
−
h
)
h
2
\dfrac{f(a+h)-2f(a)+f(a-h)}{h^{2}}
h
2
f
(
a
+
h
)
−
2
f
(
a
)
+
f
(
a
−
h
)
c)
f
(
a
+
h
)
−
f
(
a
−
h
)
2
h
\dfrac{f(a+h)-f(a-h)}{2h}
2
h
f
(
a
+
h
)
−
f
(
a
−
h
)
d)
f
(
a
+
h
)
−
f
(
a
)
h
\dfrac{f(a+h)-f(a)}{h}
h
f
(
a
+
h
)
−
f
(
a
)
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