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If $6 x - x^{2} + 12$ attains its extreme value $β$ at $x = α$ then $β =$

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$7 α$

$5 α$

$3 α$

$α$

answer is A.

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Detailed Solution

$\begin{array}{l} (x) = 6 x - x^{2} + 12 \\ f^{'} (x) = 6 - 2 x = 0 \Rightarrow x = 3 \\ β = 6 (3) - 3^{2} + 12 \\ = 21 = 7 \times 3 \\ \Rightarrow α \end{array}$

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