Dear Colleagues,

Could you please help me to solve the following problem:

The space $\displaystyle C^{1}[a,b]$ is the subspace of $\displaystyle C[a,b]$ consists of all continuously differentiable functions. Let $\displaystyle f$ be a functional defined on $\displaystyle C^{1}[a,b]$ given by $\displaystyle f(x)=x^{'}(c),c=(a+b)/2$ where $\displaystyle x\in C^{1}[a,b]$. Prove that $\displaystyle f$ is not bounded.

Regards,

Raed.