Based on the given conditions: $f(x) = x^3$ , $g(4) = 9$ , $g(2) = -9$ , and $g(0) = -\frac{1}{3}$ , along with the product rule constraint, we can determine that $g(x) = \frac{27}{(x^3-3)^3}$ .

Indefinite Integration

Product Rule and Integration

Grade None

Question:

The function g(x) is

(A) $\frac{3}{(x^3-3)^3}$

(B) $\frac{4}{(x^3-3)^3}$

(C) $\frac{9}{(x^3-3)^3}$

(D) $\frac{27}{(x^3-3)^3}$

Step-by-Step Solution

Key Concept: Use the product rule condition and the given boundary values to determine the functional form of g(x).

Based on the given conditions: $f(x) = x^3$, $g(4) = 9$, $g(2) = -9$, and $g(0) = -\frac{1}{3}$, along with the product rule constraint, we can determine that $g(x) = \frac{27}{(x^3-3)^3}$.

Correct Answer: D

Question:

Step-by-Step Solution

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