Question 4, let g(x)=x? , f(ξ) derivative /g(ξ) derivative = [f (1)-f (0)]/[g (1)-g (0)], the proof of Cauchy mean value theorem.

The fifth question, from the conclusion of the fourth question, the left side of the equation =f(a)-f(b)/(a-b), and then proved by Lagrange mean value theorem.