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Mathematics
Problem
Which of the following best defines the average rate of change of a differentiable function
f
f
f
on the closed interval
[
a
,
b
]
[a,b]
[
a
,
b
]
? a)
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
h
\displaystyle\lim_{h\to0}\frac{f(a+h)-f(a)}{h}
h
→
0
lim
h
f
(
a
+
h
)
−
f
(
a
)
b)
f
(
b
)
−
f
(
a
)
b
−
a
\displaystyle\frac{f(b)-f(a)}{b-a}
b
−
a
f
(
b
)
−
f
(
a
)
c)
1
b
−
a
∫
a
b
f
(
x
)
d
x
\displaystyle\frac{1}{b-a}\int_{a}^{b} f(x)\,dx
b
−
a
1
∫
a
b
f
(
x
)
d
x
d)
f
(
a
)
−
f
(
b
)
b
−
a
\displaystyle\frac{f(a)-f(b)}{b-a}
b
−
a
f
(
a
)
−
f
(
b
)
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