Question: Use the Extreme Value Theorem to show that each of the following functions has a positive maximum on the interval 0 x 1.

Use the Extreme Value Theorem to show that each of the following functions has a positive maximum on the interval 0 ≤ x ≤ 1.
1. f(x) = x(x - 1)ex.
2. f(x) = ex - xex.
3. f(x) = 5x(l - x)(2 - x) - 1.
4. f(x) = 8x(l - x)2 - 1.

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