Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Polynomial Functions
Derivatives
Critical Points
Concavity

Formulas

First derivative: G'(x) = 4x^3 + 6x^2 - 6x - 4
Second derivative: G''(x) = 12x^2 + 12x - 6

Theorems

Critical points occur where the first derivative equals zero
Concavity is determined by the second derivative

Suitable Grade Level

Grades 10-12 (High School Calculus)

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