Connecting a Function and Its Derivatives
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the second derivative of
f
(
x
)
=
sin
(
x
)
f(x) = \text{sin}(x)
f
(
x
)
=
sin
(
x
)
?
QUESTION
If
f
′
′
(
x
)
=
0
f''(x) = 0
f
′′
(
x
)
=
0
, what can be inferred about
f
(
x
)
f(x)
f
(
x
)
?
QUESTION
What is the second derivative of
f
(
x
)
=
ln
(
x
)
f(x) = \text{ln}(x)
f
(
x
)
=
ln
(
x
)
?
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ANSWER
f
′
′
(
x
)
=
−
1
x
2
f''(x) = -\frac{1}{x^2}
f
′′
(
x
)
=
−
x
2
1
. First derivative is
1
x
\frac{1}{x}
x
1
, then
−
1
x
2
-\frac{1}{x^2}
−
x
2
1
.
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