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Question Number 183464 by Mastermind last updated on 26/Dec/22
Find the Maximum value of  3x(4−x)    M.m
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{Maximum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{3x}\left(\mathrm{4}−\mathrm{x}\right) \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$
Answered by mr W last updated on 26/Dec/22
3x(4−x)≤3×(((x+4−x)/2))^2  =12  ⇒maximum =12
$$\mathrm{3}{x}\left(\mathrm{4}−{x}\right)\leqslant\mathrm{3}×\left(\frac{{x}+\mathrm{4}−{x}}{\mathrm{2}}\right)^{\mathrm{2}} \:=\mathrm{12} \\ $$$$\Rightarrow{maximum}\:=\mathrm{12} \\ $$
Commented by manolex last updated on 26/Dec/22
M.A⟩M.G  ((a+b)/2) ⟩(√(ab))  a=x  b=4−x  ((x+(4−x))/2)⟩(√(x(4−x)))  2⟩(√(x(4−x)))  4⟩x(4−x)  12⟩3x(4−x)
$${M}.{A}\rangle{M}.{G} \\ $$$$\frac{{a}+{b}}{\mathrm{2}}\:\rangle\sqrt{{ab}} \\ $$$${a}={x} \\ $$$${b}=\mathrm{4}−{x} \\ $$$$\frac{{x}+\left(\mathrm{4}−{x}\right)}{\mathrm{2}}\rangle\sqrt{{x}\left(\mathrm{4}−{x}\right)} \\ $$$$\mathrm{2}\rangle\sqrt{{x}\left(\mathrm{4}−{x}\right)} \\ $$$$\mathrm{4}\rangle{x}\left(\mathrm{4}−{x}\right) \\ $$$$\mathrm{12}\rangle\mathrm{3}{x}\left(\mathrm{4}−{x}\right) \\ $$
Answered by manxsol last updated on 26/Dec/22

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