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tmua.me Extreme Set C Paper 2 · Q12

Paper 2CalculusAlgebra

A quadratic polynomial ff with real coefficients satisfies

∫01f(x)2 dx=1,∫01f(x)f(1−x) dx=0.\int_0^1 f(x)^2\,\mathrm dx=1, \qquad \int_0^1 f(x)f(1-x)\,\mathrm dx=0.

What is the greatest possible value of f(1/2)f(1/2)?

A22\dfrac{\sqrt2}{2}
B11
C32\dfrac{\sqrt3}{2}
D62\dfrac{\sqrt6}{2}
E32\dfrac32
F324\dfrac{3\sqrt2}{4}

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