38. Show that equation 3 holds when h<0.3f(u)g(x+h)-g(x)hf(v)Inequality 3 can be proved in a similar way for h<0(see Exercise 38).Let's say h0. Then u and v are placed between x and x+h,souxisItis high vx. Since fis continuous atx,itisas follows.limh0f(u)=limuxf(u)=f(x),limh0f(v)=limvxf(v)=f(x)In accordance with 33 and the compression theorem, the following conclusions are obtained.g'(x)=limh0g(x+h)-g(x)h=f(x)