Let G(t) and H(t) be the concentrations of blood glucose and insulin at time t,respectively. Then G and H satisfy
dG/dt = f1(G,H) + E(t)
dH/dt = f2(G,H)
where E(t) represents external rate of change for G, and f1 and f2 represent internal rate of change for G and H, respectively.
It is known that after an overnight fast, the concentrations of glucose and insulinin the patient’s blood stabilize at their optimal values, i.e., G(t) = G0 (constant), H(t) = H0 (constant). Using this fact, show that f1(G0,H0) = 0 = f2(G0,H0).