The derivative is $f\prime=-5x^2+20x-15=-5(x-1)(x-3)$. The interior stationary point x = 1 is a local minimum and x = 3 a local maximum. Their values are 28/3 and 16. The limiting endpoint values at 0.5 and 3.5 are both below 16, so the maximum on the open interval is attained at x = 3 and equals 16, C.
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