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National
Hard
Calculus
10–12
What is the relative minimum value of
f
(
x
)
=
x
3
−
3
x
2
+
1
f(x) = x^3 - 3x^2 + 1
f
(
x
)
=
x
3
−
3
x
2
+
1
?
Qual é o valor do mínimo relativo de
f
(
x
)
=
x
3
−
3
x
2
+
1
f(x) = x^3 - 3x^2 + 1
f
(
x
)
=
x
3
−
3
x
2
+
1
?
Answer options
A.
-1
B.
-3
C.
1
D.
2
Check Answer
Solution
Step 1 of 3
1.
f
′
(
x
)
=
3
x
2
−
6
x
=
3
x
(
x
−
2
)
f'(x) = 3x^2 - 6x = 3x(x - 2)
f
′
(
x
)
=
3
x
2
−
6
x
=
3
x
(
x
−
2
)
, so the zeros are
x
=
0
x = 0
x
=
0
and
x
=
2
x = 2
x
=
2
.
Next step
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