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# Step-by-Step Math Answer

Subtract 13
*
x
*
^{
2
}
from each side of the inequality.

To find the maximum value of the given function, first subtract 13
*
x
*
^{
2
}
from each side of the given inequality.

*
x
*
^{
4
}
– 13
*
x
*
^{
2
}
+ 36
0

Factor the trinomial.

Factor the trinomial.

(
*
x
*
– 3)(
*
x
*
– 2)(
*
x
*
+ 2)(
*
x
*
+ 3)
0

So,

–3
*
x
*
2 or 2
*
x
*
3.

Find
*
f
*
′ (
*
x
*
).

Find
*
f
*
′ (
*
x
*
).

*
f
*
′ (
*
x
*
) = 3
*
x
*
^{
2
}
– 3.

Equate
*
f
*
′ (
*
x
*
) to 0.

Equate
*
f
*
′ (
*
x
*
) to 0.

3
*
x
*
^{
2
}
– 3 = 0

Factor the binomial.

Factor the binomial.

3(
*
x
*
+ 1)(
*
x
*
– 1) = 0

Set each factor equal to 0.

Set each factor equal to 0.

*
x
*
+ 1 = 0

or

*
x
*
– 1 = 0

Solve the equations.

Solve the equations.

*
x
*
= 1

or

*
x
*
= –1

So,
*
f
*
is increasing on (–
, –1) and (1,
).

Therefore,
*
f
*
is increasing on [–3, –2] and [2, 3].

Find
*
f
*
(–2).

To find
*
f
*
(–2), first substitute –2 for
*
x
*
in the given function.

*
f
*
(–2) = (–2)
^{
3
}
– 3(–2)

Next, simplify.

*
f
*
(–2) = –2

Find
*
f
*
(3).

To find
*
f
*
(3), first substitute 3 for
*
x
*
in the given function.

*
f
*
(3) = (3)
^{
3
}
– 3(3)

Next, simplify.

*
f
*
(3) = 18

So, the maximum value of the given function is 18.