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Q3Section A (Section A)3 of 60

Maximum of a parameterized determinant

Let f:R→Rf:\mathbb{R}\to\mathbb{R} be the function defined by f(x)=det⁡(1+x99 91+x9 991+x).f(x)=\det \begin{pmatrix} 1+x & 9 & 9 \ 9 & 1+x & 9 \ 9 & 9 & 1+x \end{pmatrix}. Then the maximum value of ff on the interval [9,10][9, 10] equals

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