Find the x-coordinate of the stationary points on the curve y = x^(n) e^(-x), where n is a positive integer. Determine the nature of these stationary points, distinguishing between the cases when n is odd and when n is even.

Question

anonymous · Answer

$$\frac{ dy }{ dx } = \frac{ nx ^{n-1} }{ e^x } -e ^{-x}x^n$$
$$\frac{ dy }{ dx }= \frac{ x ^{n-1} }{ e^x } (n-x)$$
$$0=\frac{ x ^{n-1} }{ e^x } (n-x)$$
Can you work the rest out?