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

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Answer 1 · 2016-07-17T17:12:39

None

#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