Final answer:
The derivative function f'(x) of f(x) = 8 - 5x³, using the power rule of differentiation, is c. f'(x) = -15x².
Step-by-step explanation:
To compute the derivative function f'(x) algebraically for the function f(x) = 8 - 5x³, we apply the power rule of differentiation. The power rule states that the derivative of x^n, with respect to x, is n*x^(n-1). Hence, the derivative of -5x³ with respect to x is -15x^2. Therefore, f'(x), the derivative of f(x), is -15x^2 since the derivative of a constant (which is 8 in this case) is zero.
The correct answer is c. f'(x) = -15x².