Question

Answer 1

A = -3(x - 1/3)^2 + 1/3 <= 1/3

--> MaxA = 1/3 <=> x = 1/3 (thỏa)

 

Answer 2

Lời giải:

$A=x(2-3x)=\frac{1}{3}-3(x^2-\frac{2}{3}x+\frac{1}{9})=\frac{1}{3}-3(x-\frac{1}{3})^2\leq \frac{1}{3}$ với mọi $0\leq x\leq \frac{2}{3}$
Vậy $A_{\max}=\frac{1}{3}$ khi $x-\frac{1}{3}=0\Leftrightarrow x=\frac{1}{3}$

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Áp dụng BĐT Cô-si ngược dấu:

$2B=2x(1-x)(1-x)\leq \left(\frac{2x+1-x+1-x}{3}\right)^3=\frac{8}{27}$

$\Rightarrow B\leq \frac{4}{27}$

Vậy $B_{\max}=\frac{4}{27}$ khi $x=\frac{1}{3}$