Math Problem Statement
f(x)=x^3+4.5x^2-12x-1. find the relative maxima of f'(x)
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Critical Points
Second Derivative Test
Formulas
f'(x) = 3x^2 + 9x - 12
Second Derivative: f''(x) = 6x + 9
Quadratic Equation: x^2 + 3x - 4 = 0
Theorems
Second Derivative Test: f''(x) > 0 implies local minimum, f''(x) < 0 implies local maximum
Suitable Grade Level
Grades 11-12
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