Final answer:
The smallest possible value of x for the equation 3x^3 = 15 is the negative cube root of 5, which is not listed in the provided options, indicating that none of the choices are correct.
Step-by-step explanation:
To find the smallest possible value of x when 3x^3 = 15, we start by dividing both sides of the equation by 3, which gives us x^3 = 5. To solve for x, we take the cube root of both sides, yielding x = √[3]{5}. Since we are looking for the smallest possible value, we consider the negative cube root as well, which is x = -√[3]{5}. Therefore, the smallest possible value of x that satisfies the equation is negative, and among the options given, the closest value to -√[3]{5} without going over is -2, which is not listed among the options provided. Thus, none of the provided choices are correct.