Second Derivative Test
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find the critical points of
f
(
x
)
=
x
3
−
3
x
2
+
2
f(x) = x^3 - 3x^2 + 2
f
(
x
)
=
x
3
−
3
x
2
+
2
.
QUESTION
Determine the extremum type for
f
(
x
)
=
x
2
−
4
x
f(x) = x^2 - 4x
f
(
x
)
=
x
2
−
4
x
at
x
=
2
x = 2
x
=
2
.
QUESTION
If
f
′
′
(
x
)
=
15
x
−
5
f''(x) = 15x - 5
f
′′
(
x
)
=
15
x
−
5
, find the concavity at
x
=
1
x = 1
x
=
1
.
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ANSWER
Concave up since
f
′
′
(
1
)
=
10
>
0
f''(1) = 10 > 0
f
′′
(
1
)
=
10
>
0
. Substituting
x
=
1
x = 1
x
=
1
gives
f
′
′
(
1
)
=
15
(
1
)
−
5
=
10
>
0
f''(1) = 15(1) - 5 = 10 > 0
f
′′
(
1
)
=
15
(
1
)
−
5
=
10
>
0
.
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