Functions of the formf(x) = xnexn! , x> 0where n is a positive integer, arise in the
Chapter 4, Problem 80(choose chapter or problem)
Functions of the form
\(f(x)=\frac{x^{n} e^{-x}}{n !}, \quad x>0\)
where n is a positive integer, arise in the statistical study of traffic flow.
(a) Use a graphing utility to generate the graph of \(f\) for \(n=2,3,4\) and \(5\), and make a conjecture about the number and locations of the relative extrema of \(f\).
(b) Confirm your conjecture using the first derivative test.
Equation Transcription:
Text Transcription:
f(x) = x^n e^−x/n! , x > 0
f
n = 2, 3, 4,
5
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