Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Derivatives
Monotonicity
Critical Points
Polynomial Functions
Formulas
First derivative test: f'(x) > 0 (increasing), f'(x) < 0 (decreasing)
Solving f'(x) = 0 to find critical points
Factoring quadratic equations
Theorems
First derivative test
Sign test for intervals of monotonicity
Suitable Grade Level
Grades 11-12 (High School Calculus)
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