F(x)=f(x)/x^2,f(x)在[a,b]连续,在(a,b)可导,如何证明F(x)在[a,b]连续,在(a,b)可导?想不通,因为我基础比较差,

问题：F(x)=f(x)/x^2,f(x)在[a,b]连续,在(a,b)可导,如何证明F(x)在[a,b]连续,在(a,b)可导?想不通,因为我基础比较差,

答案：↓↓↓

陈琦的回答：

网友采纳　　令f(x)=(∫baf(t)dt)x^2-(2∫ba1dt)x+(∫ba1/f(t)dt),则：f(x)=∫baf(t)x^2dt-2∫baxdt+∫ba1/f(t)dt=∫ba[f(t)x^2-2x+1/f(t)]dt=∫ba{[f(t)^0.5x-1/f(t)^0.5]^2}dt≥0故这个关于x的...