I have given the function$\displaystyle f(x)=x^{2}e^{13x}$ and it asks me to indicate the points of inflection and where the function is concave up(CU) or concave down(CD);

I proceded with the first derivative f'(x)=e^(13x)*x(13x+2),

- the second f"(x)=e^(13x)*[169x^(2)+52x+2],

since e^x is never 0, this one gives me[169x^(2)+52x+2]=0 for x=[-(52)+(sqrt(1352))]/(2*169) and x=[-(52)-(sqrt(1352))]/(2*169);

it bugs that those points are quite bizarre and on all the intervals the function gives me CU, does that mean that I don't have inflection points here, I might have mistaken something...

Thanks