Question

find the coordinates of the absolute maximum point for the curve y=xe^(-kx) where k is a fixed positive number. a) ((1/k), (1/ke)) b) ((-1/k),(-e/k)) c) ((1/k),(1/e^k)) d) (0,0) e) there is no maximum

Answer 1

y'= xe^(-kx)(-k)+e^(-kx)=0
e^(-kx)[-kx+1]=0
x=1/k
y''=e^(-kx)(-k)[-kx+1]+e^(-kx)(-k)
=e^(-kx)[-kx+1-k]<0 for x=1/k

Answer 2

A)