Differentiating Inverse Functions
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find
(
f
−
1
)
′
(
4
)
(f^{-1})'(4)
(
f
−
1
)
′
(
4
)
given
f
(
2
)
=
4
f(2)=4
f
(
2
)
=
4
and
f
′
(
2
)
=
5
f'(2)=5
f
′
(
2
)
=
5
.
QUESTION
What is the geometric meaning of inverse derivatives: how do the tangent line slopes compare at inverse points?
QUESTION
Find
(
f
−
1
)
′
(
9
)
(f^{-1})'(9)
(
f
−
1
)
′
(
9
)
given
f
(
3
)
=
9
f(3)=9
f
(
3
)
=
9
and
f
′
(
3
)
=
0
f'(3)=0
f
′
(
3
)
=
0
.
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ANSWER
Undefined because
f
′
(
3
)
=
0
f'(3)=0
f
′
(
3
)
=
0
. Cannot divide by zero when
f
′
(
3
)
=
0
f'(3)=0
f
′
(
3
)
=
0
.
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