Math Problem Statement
the relative maximum value of the function x^3+6x^2+3x+32
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Quadratic Equations
Critical Points
Formulas
First derivative: f'(x) = 3x^2 + 12x + 3
Quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / 2a
Second derivative: f''(x) = 6x + 12
Theorems
Critical Points Theorem
Second Derivative Test
Suitable Grade Level
Grades 11-12
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