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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