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Mathematics
Problem
The values of
a
a
a
for which the function
(
a
+
2
)
x
3
−
3
a
x
2
+
9
a
x
−
1
(a + 2)x^3 - 3ax^2 + 9ax - 1
(
a
+
2
)
x
3
−
3
a
x
2
+
9
a
x
−
1
decreases monotonically throughout for all real
x
x
x
, are (a)
a
<
−
2
a < -2
a
<
−
2
(b)
a
>
−
2
a > -2
a
>
−
2
(c)
−
3
<
a
<
0
-3 < a < 0
−
3
<
a
<
0
(d)
−
∞
<
a
≤
−
3
-\infty < a \le -3
−
∞
<
a
≤
−
3
(a)
a
<
−
2
a < -2
a
<
−
2
(b)
a
>
−
2
a > -2
a
>
−
2
(c)
−
3
<
a
<
0
-3 < a < 0
−
3
<
a
<
0
(d)
−
∞
<
a
≤
−
3
-\infty < a \le -3
−
∞
<
a
≤
−
3
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