Final answer:
The original question contains typographical errors and does not provide enough information to determine the derivative of the function f(x) at x=1. Typical methods, such as the power rule, cannot be applied without the correct function form. Therefore, it's not possible to confidently select an answer from the given choices.
Step-by-step explanation:
The given question requires us to find the derivative of the function f(x) at the point x=1. We are given the conditions of the function: 66 f(x) 8x2(f(x))3 = 0 and f(1) = -2. Since the equation provided seems to contain typographical errors, we cannot directly use it to find the derivative. However, we can use the given value f(1) = -2 to calculate the derivative using other given details or common derivative rules.
Since we are not provided with the explicit function form and based on the information given, we cannot solve for the derivative explicitly. However, if the original function was intended to be represented by f(x) = 8x2 for example, we can use the power rule for differentiation which states that if f(x) = xn, then f'(x) = nxn-1. Applying the power rule to f(x) = 8x2, we get f'(x) = 16x. Substituting x = 1 gives f'(1) = 16, which is not listed in the provided answer choices. This discrepancy indicates that there is crucial information missing that is required to solve the problem.