f(x) := a/12*x^4+b/6*x^3+c/2*x^2+d*x+e;
g(x) := diff(f(x),x,2);
L : solve(g(x)=0,x);
h(x) := (f(rhs(L[1]))-f(rhs(L[2])))/(rhs(L[1])-rhs(L[2]))*(x-rhs(L[1]))+f(rhs(L[1]));
M : solve(h(x)-f(x)=0,x);
u : sqrt((rhs(L[2]) - rhs(L[1]))^2+(f(rhs(L[2]))-f(rhs(L[1])))^2);
v : sqrt((rhs(M[4])-rhs(L[2]))^2+(f(rhs(M[4]))-f(rhs(L[2])))^2);
u/v;