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Mathematics
Problem
For a differentiable function
f
f
f
, which of the following expressions gives the average rate of change of
f
f
f
on the interval
[
a
,
a
+
h
]
[a, a+h]
[
a
,
a
+
h
]
where
h
≠
0
h\neq 0
h
=
0
? a)
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
h
\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{h}
h
→
0
lim
h
f
(
a
+
h
)
−
f
(
a
)
b)
f
(
a
+
h
)
−
f
(
a
)
h
\displaystyle \frac{f(a+h)-f(a)}{h}
h
f
(
a
+
h
)
−
f
(
a
)
c)
f
(
a
+
h
)
−
f
(
a
)
a
+
h
\displaystyle \frac{f(a+h)-f(a)}{a+h}
a
+
h
f
(
a
+
h
)
−
f
(
a
)
d)
f
(
a
+
h
)
−
f
(
a
−
h
)
2
h
\displaystyle \frac{f(a+h)-f(a-h)}{2h}
2
h
f
(
a
+
h
)
−
f
(
a
−
h
)
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