Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Concavity
Inflection Points
Product Rule
Derivative

Formulas

f'(x) = -e^x (x - 1)
f''(x) = -x e^x

Theorems

Product Rule for Derivatives
Concavity and Inflection Points using Second Derivative

Suitable Grade Level

Undergraduate Calculus