- Thread starter
- Moderator
- #1

- Jan 26, 2012

- 995

-----

**Problem**: Let $W$ be the vector space of all differentiable real-valued functions on the interval $[0,1]$. For $f,g\in W$, define

\[\langle f,g\rangle=\int_0^1 f(x)g(x)\,dx + \int_0^1 f^{\prime}(x)g^{\prime}(x)\,dx.\]

Prove that $\langle f,g\rangle$ is an inner product on $W$.

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!