Let $0 \le x \le 1.$  Find the maximum value of
\[x (1 - x)^5.\]
Question:
Let $0 \le x \le 1.$  Find the maximum value of
\[x (1 - x)^5.\]
Answer:
Let's think step by step.

user
\frac{3125}{46656}
Let $0 \le x \le 1.$  Find the maximum value of
\[x (1 - x)^5.\]
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