Math Problem Statement
Let f(x) = x³-3x² + 4 sin(x)ex. Identify which critical points correspond to local maxima, and describe the behavior of f(x) as it approaches ±∞.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Critical Points
Derivatives
Transcendental Equations
Second Derivative Test
Formulas
f'(x) = 3x^2 - 6x + 4e^x(sin(x) + cos(x))
f''(x) = 6x - 6 + 4e^x(2cos(x))
Theorems
Second Derivative Test
Limit Theorems for Behavior at Infinity
Suitable Grade Level
University level (Calculus II or III)