In terms of the last term in the trapezoid method recurrence formula, prove that

there exists wi $<$ c $<$ wi $+$ hf$($wi$)$ such that f$($wi $+$ hf$($wi$))=$ f$($wi$)+$ hf$($wi$)$f$\text{'}($wi$)+$ h$^2/2[$f$($wi$)]^2$f$\text{'}\text{'}($c$).$