Given a function f which satisfies the differential equation xf^('')(x)+3x(f^(')(x))^(2)=1-e^(-x) for all x.(No need to solve the DE)(1) If f has an extremum at the point of c!=0, show that this extremum is minimum. (2) If f has an extremum at 0, is it maximum or minimum? (3) if f(0)=f^(')(0)=0, find the smallest constant \Lambda such that f(x)=Ax^(2) for all x>=0