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Mathematics
Problem
A function
g
g
g
is defined only for
x
≥
2
x\ge 2
x
≥
2
. To approximate
g
′
(
2
)
g'(2)
g
′
(
2
)
using nearby function values of
g
g
g
, which of the following expressions is MOST appropriate? (Assume
h
>
0
h>0
h
>
0
is small.) a)
g
(
2
+
h
)
−
g
(
2
−
h
)
2
h
\dfrac{g(2+h)-g(2-h)}{2h}
2
h
g
(
2
+
h
)
−
g
(
2
−
h
)
b)
g
(
2
+
h
)
−
g
(
2
)
h
\dfrac{g(2+h)-g(2)}{h}
h
g
(
2
+
h
)
−
g
(
2
)
c)
g
(
2
+
h
)
−
g
(
2
)
2
h
\dfrac{g(2+h)-g(2)}{2h}
2
h
g
(
2
+
h
)
−
g
(
2
)
d)
g
(
2
+
2
h
)
−
g
(
2
+
h
)
h
\dfrac{g(2+2h)-g(2+h)}{h}
h
g
(
2
+
2
h
)
−
g
(
2
+
h
)
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