find the critical points of the function f(x)=4x⁶-6x⁴
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Calculus Examples
Popular Problems Calculus Find the Critical Points f(x)=2x^6-6x^4
f
(
x
)
=
2
x
6
−
6
x
4
Find the derivative.
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12
x
5
−
24
x
3
Set the derivative equal to
0
.
12
x
5
−
24
x
3
=
0
Solve for
x
.
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x
=
0
,
√
2
,
−
√
2
Substitute the values of
x
which cause the derivative to be
0
into the original function.
f
(
0
)
=
2
(
0
)
6
−
6
(
0
)
4
f
(
√
2
)
=
2
(
√
2
)
6
−
6
(
√
2
)
4
f
(
−
√
2
)
=
2
(
−
√
2
)
6
−
6
(
−
√
2
)
4
Evaluate.
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f
(
0
)
=
0
f
(
√
2
)
=
−
8
f
(
−
√
2
)
=
−
8
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
x
|
x
∈
R
}
Since there are no values of
x
where the derivative is undefined, there are no additional critical points.
(
0
,
0
)
,
(
√
2
,
−
8
)
,
(
−
√
2
,
−
8
)