An inflection point of gx xe2x occurs at x 7 x 1 5 x 2

An inflection point of g(x) = xe^2x occurs at x = _ (7) x = 1 (5) x = 2 (9) x = 0 (2) x = e^-2 (6) there is no inflection point

Solution

given g(x) = xe^-2x

g\'(x) = e^-2x - 2xe^-2x

g\'\'(x) = -2e^-2x - 2e^-2x + 4xe^-2x = - 4e^-2x + 4xe^-2x

for inflelction point g\'\'(x) = 0

  - 4e^-2x + 4xe^{-2x = 0}

   - 4e^-2x(1 - x) = 0

1 - x =0 and e^-2x = 0

x= 1