Suppose that f,g,h are real valued functions on (a,b) and (a,b). Assume that f and h are differentiable at , f( )=h( ) and f(x)<=g(x)<=h(x) for all x (a,b). show that g is differentiable at and f'( )=g'( )=h'( ). Use this result to explain why the fraction F(x) defined by F(x)= sin(1/x), x not equal to 0, and F(0)=0 has derivative equal to 0 at x=0.
I honestly have no clue I hope some one can help me thanks!