If f is a real-valued function of one real variable which has a continuous derivative on the closed interval [a,b] and for which there is no x∈[a,b] such that f(x)=f′(x)=0, then prove that there is a function g with continuous first derivative on [a,b] such that fg′−f′g is positive on [a,b]. Putnamfunctioncalculusderivative