Question
If Rolle’s theorem holds for the function f(x) = (x – 2) log x, x ∈ [1, 2], show that the equation x log x = 2 – x is satisfied by at least one value of x in (1, 2).
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$\left|\begin{array}{lll}1 & 3 & 6 \\ 6 & 1 & 4 \\ 3 & 7 & 12\end{array}\right|+4\left|\begin{array}{lll}2 & 3 & 3 \\ 2 & 1 & 2 \\ 1 & 7 & 6\end{array}\right|=10\left|\begin{array}{lll}1 & 2 & 1 \\ 3 & 1 & 7 \\ 3 & 2 & 6\end{array}\right|$
$\sin \left(29^{\circ} 30^{\circ}\right)$, given that $1^{\circ}=0.0175^{\circ}, \sqrt{ } 3=1.732$.