High School

Given the derivative function [tex]f'(x) = 3x^3 + 9x^2 + 18x[/tex], choose the correct original function \(f(x)\) from the options below:

A. [tex]x^2 + 8x[/tex]

B. [tex]x^3 + 9x^2 + 18x[/tex]

C. [tex]3x^3 + 9x^2 + 18x[/tex]

D. [tex]x^3 - 9x^2 + 18x[/tex]

Answer :

Final answer:

The problem requires knowledge of integration to identify the original function from its derivative. The original function can be found by integrating the given derivative function.

Explanation:

The question seems to present a function f'(x) = 3x³ + 9x² + 18x and asks for possible forms of the original function f(x). However, given equations don't lead to a definitive conclusion. We could only identify the original function by integrating the given function, f'(x). This is a key concept in calculus and requires knowledge of integration rules. For example, the integral of x³ is (1/4)x⁴ and the integral of x² is (1/3)x³, and so on.Integration, calculus, and polynomial functions are key topics related to this problem.

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