Math Problem Statement

y=x^4-16x^2

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Functions
Factoring
Critical Points
Sign Analysis
Concavity

Formulas

y = x^4 - 16x^2 = x^2(x - 4)(x + 4)
First derivative: dy/dx = 4x^3 - 32x
Second derivative: d^2y/dx^2 = 12x^2 - 32

Theorems

Difference of Squares
Critical Points
Second Derivative Test

Suitable Grade Level

Grades 11-12