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Mathematics
Mathematics
Problem
Let the function
f
(
x
)
=
2
x
3
+
(
2
p
−
7
)
x
2
+
3
(
2
p
−
9
)
x
−
6
f(x) = 2x^3 + (2p - 7)x^2 + 3(2p - 9)x - 6
f
(
x
)
=
2
x
3
+
(
2
p
−
7
)
x
2
+
3
(
2
p
−
9
)
x
−
6
have a maxima for some value of
x
<
0
x < 0
x
<
0
and a minima for some value of
x
>
0
x > 0
x
>
0
. Then, the set of all values of
p
p
p
is A
(
9
2
,
∞
)
\left(\frac{9}{2}, \infty\right)
(
2
9
,
∞
)
B
(
0
,
9
2
)
\left(0, \frac{9}{2}\right)
(
0
,
2
9
)
C
(
−
∞
,
9
2
)
\left(-\infty, \frac{9}{2}\right)
(
−
∞
,
2
9
)
D
(
−
9
2
,
9
2
)
\left(-\frac{9}{2}, \frac{9}{2}\right)
(
−
2
9
,
2
9
)
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