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.
- myisland8132Lv 71 decade agoFavorite Answer
H(x)=cx-∫ (x0->x) f(s)ds
H'(x)=c-f(x) ,so H'(x)=0=>f(x) = c
Since if H:I→R has a local extreme point, then the critical point M should satisfied H'(M) = 0 => f(M) = c and thus c is the image of f:I→R