Tìm min max hàm số.

D

dien0709

$y=(sin^2x+cos^2x)^2-2sin^2xcos^2x+asinxcosx=-2sin^2xcos^2x+asinxcosx+1$

$t=sinxcosx=\dfrac{sin2x}{2}\to -\dfrac{1}{2}\le t\le \dfrac{1}{2}$

$\to f(t)=\dfrac{a^2}{8}+1-2(t-\dfrac{a}{4})^2\le \dfrac{a^2}{8}+1$

$f(-\dfrac{1}{2})=\dfrac{1-a}{2}$ , $f(\dfrac{1}{2})=\dfrac{a+1}{2}$

$\to max y=\dfrac{a^2}{8}+1$ \Leftrightarrow $t=\dfrac{a}{4}$

$ min y=min(\dfrac{1-a}{2};\dfrac{a+1}{2})$
 
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