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1. Minimum ratio of derivative energy to squared mean ●●●●○ 100 ptsLet $f$ be a continuously differentiable real-valued function on $[0,1]$ with $\int_{1/3}^{2/3} f(x)\,dx = 0$. Find the minimum value of $\dfrac{\int_0^1 (f'(x))^2\,dx}{\left(\int_0^1 f(x)\,dx\right)^2}$ over all such $f$ for which the denominator is nonzero.