## decompose the difference g(y)-g(y') help!

Hi,
i have a puzzling question that i have been trying to solve for hours over the last couple of days.

i want to know why i can always decompose the difference between g(y)-g(y') when g is a differentiable function where:
g(y)-g(y')=Q(y,y')(y-y'), where Q(y,y') is continuous.