Final answer:
The absolute maximum of the function f(x) = 32x - 4x^2 + 11 on the interval [0, 8] is not listed among the options provided. Upon evaluating the function at critical point and endpoints, the maximum value determined is 75 at x = 4.
Step-by-step explanation:
To find the absolute maximum of the function f(x) = 32x - 4x^2 + 11 on the interval [0, 8], we first differentiate the function to find any critical points. The derivative of f(x) is f'(x) = 32 - 8x. Setting the derivative equal to zero gives us f'(x) = 0 which implies 32 - 8x = 0, or x = 4.
Next, we evaluate the function at the critical point and the endpoints of the interval. f(0) = 11, f(4) = 32(4) - 4(4)^2 + 11 = 128 - 64 + 11 = 75, and f(8) = 32(8) - 4(8)^2 + 11 = 256 - 256 + 11 = 11.
Comparing these values, we see that the absolute maximum value of the function on the given interval is at x = 4, which is 75. Therefore, none of the provided options A: 8, B: 4, C: 0, or D: 11 are correct; the absolute maximum value is 75.