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Question Number 183465 by Mastermind last updated on 26/Dec/22
Find the least value of   (1−2x)(1−x).    M.m
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\left(\mathrm{1}−\mathrm{2x}\right)\left(\mathrm{1}−\mathrm{x}\right). \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$
Answered by mr W last updated on 26/Dec/22
(1−2x)(1−x)=0  ⇒x_1 =(1/2), x_2 =1  minimum at x=(((1/2)+1)/2)=(3/4)  minimum=(1−((2×3)/4))(1−(3/4))=−(1/8) ✓
$$\left(\mathrm{1}−\mathrm{2}{x}\right)\left(\mathrm{1}−{x}\right)=\mathrm{0} \\ $$$$\Rightarrow{x}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}},\:{x}_{\mathrm{2}} =\mathrm{1} \\ $$$${minimum}\:{at}\:{x}=\frac{\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${minimum}=\left(\mathrm{1}−\frac{\mathrm{2}×\mathrm{3}}{\mathrm{4}}\right)\left(\mathrm{1}−\frac{\mathrm{3}}{\mathrm{4}}\right)=−\frac{\mathrm{1}}{\mathrm{8}}\:\checkmark \\ $$
Commented by manolex last updated on 26/Dec/22
$$ \\ $$$$ \\ $$$$ \\ $$

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