Suppose f,g, & h are defined on (a,b) & a<x0<b. Assume f and h are differentiable at x0, f(x0)=h(x0), & f(x)<g(x)<h(x) for all x in (a,b). Prove that g is differentiable at x0 and f'(x0)=g'(x0)=g'(x0).
Suppose f,g, & h are defined on (a,b) & a<x0<b. Assume f and h are differentiable at x0, f(x0)=h(x0), & f(x)<g(x)<h(x) for all x in (a,b). Prove that g is differentiable at x0 and f'(x0)=g'(x0)=g'(x0).
It is important that so .
If can you show that
There is a similar statement if .
Those are used on the limit definition of the derivatives and .