Second Derivative Test
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Determine the nature of the extremum at
x
=
1
2
x = \frac{1}{2}
x
=
2
1
for
f
(
x
)
=
−
x
2
+
x
f(x) = -x^2 + x
f
(
x
)
=
−
x
2
+
x
.
QUESTION
What is the second derivative of
f
(
x
)
=
3
x
4
−
8
x
2
+
5
f(x) = 3x^4 - 8x^2 + 5
f
(
x
)
=
3
x
4
−
8
x
2
+
5
?
QUESTION
What is the second derivative of
f
(
x
)
=
−
x
4
+
2
x
2
−
x
f(x) = -x^4 + 2x^2 - x
f
(
x
)
=
−
x
4
+
2
x
2
−
x
?
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ANSWER
f
′
′
(
x
)
=
−
12
x
2
+
4
f''(x) = -12x^2 + 4
f
′′
(
x
)
=
−
12
x
2
+
4
. Differentiate
f
′
(
x
)
=
−
4
x
3
+
4
x
−
1
f'(x) = -4x^3 + 4x - 1
f
′
(
x
)
=
−
4
x
3
+
4
x
−
1
to get the second derivative.
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