Because the maximum values are equal, let f(x) get the maximum value at x 1, and g(x) get the maximum value at x2, a.

Then h(x 1)≥0, and h(x2)≤0. If x 1=x2, it is recorded as c, and h (c) = 0; If x 1≠x2, the existence of c between x 1 and x2 (inclusive) makes h(c)=0. That is, no matter what, you can always find a < c<b that makes h(c)=0.

According to Rolle's theorem, because h(a)=h(b)=h(c)=0, there is y 1, y2, which makes A.

Applying Rolle theorem again, there exists k, y 1