# 高等微積分.....急

Let i be an open interval of real numbers and suppose that the function

f:I→R is continuous. Let c be a real number. Fix a number x0 in the interval I and define the auxiliary function H:R→R by

H(x)=cx-∫ 上限X 下限X0 f(s)ds for x in I

For a point x in I. show that f(x)=c if H`(x)=0.

conclude that c is the image of f:I→R provided that the function

H:I→R has a local extreme point.