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Mathematics
Problem
For a differentiable, invertible function
f
f
f
, suppose
(
f
−
1
)
′
(
f
(
a
)
)
(f^{-1})'(f(a))
(
f
−
1
)
′
(
f
(
a
))
exists. Which of the following must be true? a)
(
f
−
1
)
′
(
a
)
=
0
(f^{-1})'(a)=0
(
f
−
1
)
′
(
a
)
=
0
b)
f
′
(
a
)
≠
0
f'(a)\neq 0
f
′
(
a
)
=
0
c)
f
′
(
f
(
a
)
)
≠
0
f'(f(a))\neq 0
f
′
(
f
(
a
))
=
0
d)
f
′
(
a
)
=
0
f'(a)=0
f
′
(
a
)
=
0
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