If y = xe^(-x), what are the points of inflection of the graph f (x)?

1 Answer
Jul 17, 2016

None

Explanation:

y = xe^(-x)

by the product rule
y' =(x)' e^(-x) + x (e^(-x))'

= e^(-x) + x (-e^(-x))

= e^(-x) (1- x)

stationary points at y' = 0 implies x = 1

by the product rule

y'' = (e^(-x))' (1- x) + e^(-x) (1- x)'

y'' = (-e^(-x)) (1- x) + e^(-x) (-1)

=e^-x (x-2)

f''(1) = 1/e*(-1) <0 ie max

This does not have an inflexion ie f'' = 0 or f'' ndef