Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Extrema
Critical Points

Formulas

First derivative: f'(x) = 4x^3 + 64x
Second derivative: f''(x) = 12x^2 + 64
Set f'(x) = 0 for critical points
Use second derivative test for concavity

Theorems

Second Derivative Test
Critical Points Theorem

Suitable Grade Level

Grades 11-12 (Calculus Level)