Math Problem Statement

f(x) = 2xe^x. the graph is concave down when?

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Concavity
Derivatives
Exponential Functions

Formulas

f'(x) = 2e^x(1 + x)
f''(x) = 2e^x(x + 2)

Theorems

Second Derivative Test
Product Rule for Derivatives

Suitable Grade Level

Grades 11-12, Early College