Then F(b)=f(a)g(b)-f(b)g(a)

F(a)=f(a)g(a)-f(a)g(a)=0

∵f(x) and g(x) are continuous on [a, b] and differentiable on [a, b].

∴F(x)=f(a)g(x)-f(x)g(a) is continuous on [a, b] and differentiable on (a, b).

The existence of ∴∈ (a, b) makes [f(b)-f(a)]/(b-a)= f '(∴).

After that, you can get the syndrome.