Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Polynomial Functions
Derivative
Critical Points
Inflection Points

Formulas

First derivative: f'(x) = -4x^3 - 6x^2 + 6x + 4
Second derivative: f''(x) = -12x^2 - 12x + 6
Setting f'(x) = 0 for critical points
Setting f''(x) = 0 for inflection points

Theorems

Derivative Test for Critical Points
Second Derivative Test for Inflection Points

Suitable Grade Level

Grades 11-12 or Early Calculus