So let the function be defined like this: $$f:[a,b]\rightarrow\mathbb{R}, f(a)=a, f(\frac{a+b}{2})=2a, f(b)=3a$$ Also the function is double differentiable on $(a,b)$
So know i want to prove that $ \exists x_{0}$ such that $f''(x_{0})=0$
So i thought i could first use something to describe first derivative, but i somehow cannot do that, so i can't prove that for second derivative, if i don't know anything of first yet. Any help would be appreciated.