Concavity of Functions Over Their Domains
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the concavity of
f
(
x
)
=
ln
(
x
)
f(x) = \text{ln}(x)
f
(
x
)
=
ln
(
x
)
over
x
>
0
x > 0
x
>
0
?
QUESTION
Determine concavity of
f
(
x
)
=
x
3
−
x
f(x) = x^3 - x
f
(
x
)
=
x
3
−
x
at
x
=
1
x = 1
x
=
1
.
QUESTION
Identify an inflection point for
f
(
x
)
=
x
3
−
3
x
2
+
x
f(x) = x^3 - 3x^2 + x
f
(
x
)
=
x
3
−
3
x
2
+
x
.
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ANSWER
Inflection at
x
=
1
x = 1
x
=
1
where
f
′
′
(
x
)
f''(x)
f
′′
(
x
)
changes sign. Second derivative changes sign at this point.
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