For a real number $x,$ find the maximum value of
\[\frac{x^4}{x^8 + 2x^6 - 4x^4 + 8x^2 + 16}.\]
Question:
For a real number $x,$ find the maximum value of
\[\frac{x^4}{x^8 + 2x^6 - 4x^4 + 8x^2 + 16}.\]
Answer:
Let's think step by step.

user
\frac{1}{12}
For a real number $x,$ find the maximum value of
\[\frac{x^4}{x^8 + 2x^6 - 4x^4 + 8x^2 + 16}.\]
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