Final answer:
The inverse derivative of the function x³ - 3x - 1 is the reciprocal of its derivative, which results in the answer C) 1/(3x² - 3).
Step-by-step explanation:
The student is attempting to find the inverse derivative, commonly known as the integral, of the function x³ - 3x - 1. To find the integral, we need to reverse the process of differentiation. For the term x³, the integral is x⁴/4. For -3x, the integral is -3x²/2. However, we do not need to find the entire integral to answer this question. We're specifically looking for what is known as the inverse derivative or the derivative of the inverse function.
The derivative of the given function x³ - 3x - 1 is 3x² - 3. Now, the inverse derivative of a function at a given point is the reciprocal of the derivative of its inverse function at that point. Thus, the inverse derivative is 1 divided by the derivative, or 1/(3x² - 3). Therefore, the correct answer is C) 1/(3x² - 3).