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Mathematics
Problem
Let
f
(
x
)
=
x
3
f(x)=x^{3}
f
(
x
)
=
x
3
. Determine the value of
b
(
≠
1
)
b\,(\neq 1)
b
(
=
1
)
such that the average rate of change of
f
f
f
over the interval
[
1
,
b
]
[1,b]
[
1
,
b
]
equals the instantaneous rate of change at
x
=
1
x=1
x
=
1
. a)
2
2
2
b)
−
2
-2
−
2
c)
−
1
2
-\dfrac12
−
2
1
d)
−
1
-1
−
1
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