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Problem
Problem
Let
f
(
x
)
f(x)
f
(
x
)
be a cubic polynomial defined by
f
(
x
)
=
x
3
3
+
(
a
−
3
)
x
2
+
x
−
13
f(x) = \frac{x^3}{3} + (a-3)x^2 + x - 13
f
(
x
)
=
3
x
3
+
(
a
−
3
)
x
2
+
x
−
13
. Then, the sum of all possible value(s) of 'a' for which
f
(
x
)
f(x)
f
(
x
)
has negative point of local minimum in the interval
[
1
,
5
]
[1, 5]
[
1
,
5
]
, is
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