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Mathematics
Mathematics
Problem
Consider
f
(
x
)
=
x
6
−
4
x
4
+
1
f(x)=x^{6}-4x^{4}+1
f
(
x
)
=
x
6
−
4
x
4
+
1
. At
x
=
0
x=0
x
=
0
,
f
′
(
0
)
=
f
′
′
(
0
)
=
0
f'(0)=f''(0)=0
f
′
(
0
)
=
f
′′
(
0
)
=
0
. What is the nature of
x
=
0
x=0
x
=
0
? a) Point of inflection (no extremum) b) Strict local maximum c) Strict local minimum d) Cannot be decided without a graph
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