Question

An inflection point of g(x)=xe^(-2x) occurs at x =

Answer 1

inflection points occur when 2nd derivative is zero
g''(x) = 0

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

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

--> 4xe^(-2x) - 4e^(-2x) = 0
--> 4e^(-2x)(x-1) = 0
--> x = 1