For what value(s) of x does the graph of g(x)=x+10/x^3+5x^2-10x

Explanation:
First, find the derivative.
f
'
(
x
)
=
3
x
2
+
6
x
+
1
A horizontal tangent will have a slope of
0
. The derivative represents the instantaneous rate of change of a function. Set the derivative to
0
and solve for
x
.
0
=
3
x
2
+
6
x
+
1
x
=
−
6
±
√
6
2
−
4
⋅
3
⋅
1
2
⋅
3
x
=
−
6
±
√
24
6
x
=
−
6
±
2
√
6
6
x
=
−
1
±
1
3
√
6
x
=
−
3
±
√
6
Hopefully this helps!

Step-by-step explanation:

There are many integers that will satisfy the conditions mentioned. For example, -9 and -2 would satisfy both conditions. These integers are both greater than -10, and when added together, they equal -11, which is less than -10.