Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Critical Points
Second Derivative Test

Formulas

First derivative: g'(x) = 2x(3 - x)^3 - 3x^2(3 - x)^2
Second derivative test to identify maxima/minima

Theorems

Second Derivative Test

Suitable Grade Level

Grade 11-12 / College-level Calculus