Math Problem Statement
given f(x)= (x-3)^2 e^-2x, find the critical values of f, the intervals where f is increasing/decreasing, and the x values of any local extrema of f (specify the type).
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Critical Points
First Derivative Test
Increasing/Decreasing Functions
Local Extrema
Formulas
Product Rule: f'(x) = u'(x)v(x) + u(x)v'(x)
Chain Rule: d/dx[e^u(x)] = e^u(x) * u'(x)
First Derivative Test
Theorems
First Derivative Test
Suitable Grade Level
Grades 11-12 (Advanced Calculus)
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