Connecting a Function and Its Derivatives
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find
f
′
(
x
)
f'(x)
f
′
(
x
)
for
f
(
x
)
=
x
2
+
2
x
+
1
f(x) = x^2 + 2x + 1
f
(
x
)
=
x
2
+
2
x
+
1
.
QUESTION
What can be concluded if
f
′
′
(
x
)
<
0
f''(x) < 0
f
′′
(
x
)
<
0
at a point?
QUESTION
Find
f
′
′
(
x
)
f''(x)
f
′′
(
x
)
for
f
(
x
)
=
x
4
f(x) = x^4
f
(
x
)
=
x
4
.
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ANSWER
f
′
′
(
x
)
=
12
x
2
f''(x) = 12x^2
f
′′
(
x
)
=
12
x
2
. Apply power rule:
f
′
(
x
)
=
4
x
3
f'(x) = 4x^3
f
′
(
x
)
=
4
x
3
, then
f
′
′
(
x
)
=
12
x
2
f''(x) = 12x^2
f
′′
(
x
)
=
12
x
2
.
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