Consider the following function ρ (f) on W1,2[0,1]

Question

Consider the following function on $W^{1,2}[0,1]$: $$\rho (f) =|f(0)|+\int_0^1|f′| .$$

i) Show that $\rho$ is a norm on $W^{1,2}[0,1]$ equivalent to the standard norm.

ii) Find constants $c$ and $C$ such that $c\rho (f) \le \| f \|_{W^{1,2}[0,1]}\le C\rho(f)$.

For part i) I want to use the theorem:

|u|_{W^k,p[$\Omega$]}=($\Sigma$_|$\alpha$|=k||D^$\alpha$u||^p_{L^p[$\Omega$]}+$\rho$(u)^p)^1/p

but I am not sure exactly what to plug in where. I think I want to substitute my original $\rho$(f) equation in for u but am not sure what the $\rho$ in the theorem implies. Any help is appreciated.