Concavity of Functions Over Their Domains
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find
f
′
′
(
x
)
f''(x)
f
′′
(
x
)
for
f
(
x
)
=
x
3
−
3
x
2
f(x) = x^3 - 3x^2
f
(
x
)
=
x
3
−
3
x
2
and determine concavity at
x
=
2
x=2
x
=
2
.
QUESTION
Evaluate
f
′
′
(
x
)
f''(x)
f
′′
(
x
)
for
f
(
x
)
=
ln
(
x
)
f(x) = \text{ln}(x)
f
(
x
)
=
ln
(
x
)
. What does it imply for
x
>
0
x > 0
x
>
0
?
QUESTION
Find
f
′
′
(
x
)
f''(x)
f
′′
(
x
)
for
f
(
x
)
=
x
5
f(x) = x^5
f
(
x
)
=
x
5
. What is the concavity at
x
=
1
x=1
x
=
1
?
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ANSWER
Concave up.
f
′
′
(
x
)
=
20
x
3
f''(x) = 20x^3
f
′′
(
x
)
=
20
x
3
and
f
′
′
(
1
)
=
20
>
0
f''(1) = 20 > 0
f
′′
(
1
)
=
20
>
0
.
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