Sketching Graphs of Functions and Derivatives
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Determine where
f
(
x
)
=
−
x
3
+
3
x
2
f(x) = -x^3 + 3x^2
f
(
x
)
=
−
x
3
+
3
x
2
is decreasing.
QUESTION
Calculate
f
′
(
x
)
f'(x)
f
′
(
x
)
for
f
(
x
)
=
x
3
−
3
x
+
1
f(x) = x^3 - 3x + 1
f
(
x
)
=
x
3
−
3
x
+
1
.
QUESTION
Determine the local maximum of
f
(
x
)
=
−
x
2
+
4
x
−
3
f(x) = -x^2 + 4x - 3
f
(
x
)
=
−
x
2
+
4
x
−
3
.
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ANSWER
Local maximum at
x
=
2
x = 2
x
=
2
. Find critical point:
f
′
(
x
)
=
−
2
x
+
4
=
0
f'(x) = -2x + 4 = 0
f
′
(
x
)
=
−
2
x
+
4
=
0
gives
x
=
2
x = 2
x
=
2
.
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