Math Problem Statement
Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. f(x)equals=e Superscript negative x squared divided by 18e−x2/18
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Concavity
Inflection Points
Derivative
Exponential Functions
Formulas
First derivative: f'(x) = -x/9 * e^(-x^2 / 18)
Second derivative: f''(x) = e^(-x^2 / 18) * (x^2 - 9)/81
Theorems
Concavity test using second derivative
Inflection points occur where the second derivative equals zero
Suitable Grade Level
Grades 11-12 or college-level Calculus
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