Math Problem Statement

4xe^(-9x) find inflection

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Inflection Points
Product Rule

Formulas

Product rule: (fg)' = f'g + fg'
First derivative of f(x) = 4xe^{-9x}: f'(x) = e^{-9x}(4 - 36x)
Second derivative of f(x) = 4xe^{-9x}: f''(x) = 36e^{-9x}(9x - 2)

Theorems

Inflection Point Criterion: f''(x) changes sign around the point

Suitable Grade Level

Grade 11-12