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Let f be a continuously differentiable real-valued function on [0,1] such that $\int_{1/3}^{2/3} f(x)dx = 0$. Find the minimum value of $$I = \frac{\int_{0}^{1}f′(x)^2 dx} {(\int_{0}^{1}f(x)dx)^2}$$

Prince Raj
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  • What have you tried? – jgon Nov 06 '18 at 03:29
  • first of all I tried to differentiate but it was too complex. My approach was to differentiate and double differentiate and then find min value according to sign of double differentiable value. – Prince Raj Nov 06 '18 at 03:31

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