Find first and second derivatives, critical number, inflection points.
f(x) = xe^x
f'(x) = ('x) (e^x) + x(e^x)('x)
f'(x) = e^x+xe^x
f'(x) = e^x(1+x)
Critical number x = -1
f"(x) = e^x(1) + (1+x)(e^x)
f"(x) = e^x +e^x(1+x)
Critical Number x=-1
I hope I am close to the correct answer.