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TIFR ECE 2022 | Question: 13

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Calculate the minimum value attained by the function

\[\sin (\pi x)-\sqrt{2} \pi x^{2}\]

for values of $x$ which lie in the interval $[0,1]$.

  1. $\frac{1}{\sqrt{2}}\left(1-\frac{\pi}{8}\right)$
  2. $0$
  3. $1-\frac{\pi}{2 \sqrt{2}}$
  4. $-\frac{1}{\sqrt{2}}\left(1+\frac{9 \pi}{2}\right)$
  5. $-\sqrt{2} \pi$

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