![y=x^3-2x^2+x+3
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y`=3x^2-4x+1
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y`=0
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3x^2-4x+1=0
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D_1=4-3=1
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x_1=1
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x_2= \frac{1}{3}](https://tex.z-dn.net/?f=y%3Dx%5E3-2x%5E2%2Bx%2B3%0A%5C%5C%5C%0Ay%60%3D3x%5E2-4x%2B1%0A%5C%5C%5C%0Ay%60%3D0%0A%5C%5C%5C%0A3x%5E2-4x%2B1%3D0%0A%5C%5C%5C%0AD_1%3D4-3%3D1%0A%5C%5C%5C%0Ax_1%3D1%0A%5C%5C%5C%0Ax_2%3D+%5Cfrac%7B1%7D%7B3%7D+ "y=x^3-2x^2+x+3
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y`=3x^2-4x+1
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y`=0
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3x^2-4x+1=0
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D_1=4-3=1
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x_1=1
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x_2= \frac{1}{3}")
Точки 1 и 1/3 - точки экстремума
При x<1 и x>1/3 - возрастает
При 1/3<х<1 - убывает<br>y(0)=3
y(1/3)=85/81 - наименьшее
y(1)=3
y(3/2)=3.375 - наибольшее
![6sin^2x-sinx-1=0
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D=1+24=25
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sinx= \frac{1+5}{6} =1
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x= \frac{\pi}{2} +2\pi n, n\in Z
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sinx= \frac{1-5}{6}= \frac{-2}{3}
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x=(-1)^{k+1} arcsin\frac{2}{3}+\pi k, k\in Z](https://tex.z-dn.net/?f=6sin%5E2x-sinx-1%3D0%0A%5C%5C%5C%0AD%3D1%2B24%3D25%0A%5C%5C%5C%0Asinx%3D+%5Cfrac%7B1%2B5%7D%7B6%7D+%3D1%0A%5C%5C%5C%0Ax%3D+%5Cfrac%7B%5Cpi%7D%7B2%7D+%2B2%5Cpi+n%2C+n%5Cin+Z%0A%5C%5C%5C%0Asinx%3D+%5Cfrac%7B1-5%7D%7B6%7D%3D+%5Cfrac%7B-2%7D%7B3%7D%0A%5C%5C%5C%0Ax%3D%28-1%29%5E%7Bk%2B1%7D+arcsin%5Cfrac%7B2%7D%7B3%7D%2B%5Cpi+k%2C+k%5Cin+Z "6sin^2x-sinx-1=0
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D=1+24=25
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sinx= \frac{1+5}{6} =1
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x= \frac{\pi}{2} +2\pi n, n\in Z
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sinx= \frac{1-5}{6}= \frac{-2}{3}
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x=(-1)^{k+1} arcsin\frac{2}{3}+\pi k, k\in Z")
1" alt="0.5cos^2x-cosx=0
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cosx=0
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x= \frac{\pi}{2} +\pio n , n\in Z
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0.5cosx-1=0
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cosx \neq 2>1" align="absmiddle" class="latex-formula">
![6cos^2x+sin^2x-5sinxcosx=0
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tg^2x-5tgx+6=0
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D=25-24=1
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tgx= \frac{5+1}{2} =3
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x=arctg3+\pi n, n\in Z
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tgx= \frac{5-1}{2} =2
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x=arctg2+\pi n, n\in Z](https://tex.z-dn.net/?f=6cos%5E2x%2Bsin%5E2x-5sinxcosx%3D0%0A%5C%5C%5C%0Atg%5E2x-5tgx%2B6%3D0%0A%5C%5C%5C%0AD%3D25-24%3D1%0A%5C%5C%5C%0Atgx%3D+%5Cfrac%7B5%2B1%7D%7B2%7D+%3D3%0A%5C%5C%5C%0Ax%3Darctg3%2B%5Cpi+n%2C+n%5Cin+Z%0A%5C%5C%5C%0Atgx%3D+%5Cfrac%7B5-1%7D%7B2%7D+%3D2%0A%5C%5C%5C%0Ax%3Darctg2%2B%5Cpi+n%2C+n%5Cin+Z "6cos^2x+sin^2x-5sinxcosx=0
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tg^2x-5tgx+6=0
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D=25-24=1
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tgx= \frac{5+1}{2} =3
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x=arctg3+\pi n, n\in Z
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tgx= \frac{5-1}{2} =2
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x=arctg2+\pi n, n\in Z")
![sin^2(\pi-x)+cos( \frac{\pi}{2}+x)=0
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sin^2x-sinx=0
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sinx=0
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x=\pi n, n\in Z
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sinx-1=0
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sinx=1
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x= \frac{\pi}{2}+2\pi n, n\in Z](https://tex.z-dn.net/?f=sin%5E2%28%5Cpi-x%29%2Bcos%28+%5Cfrac%7B%5Cpi%7D%7B2%7D%2Bx%29%3D0%0A%5C%5C%5C%0A+sin%5E2x-sinx%3D0%0A%5C%5C%5C%0Asinx%3D0%0A%5C%5C%5C%0Ax%3D%5Cpi+n%2C+n%5Cin+Z%0A%5C%5C%5C%0Asinx-1%3D0%0A%5C%5C%5C%0Asinx%3D1%0A%5C%5C%5C%0Ax%3D+%5Cfrac%7B%5Cpi%7D%7B2%7D%2B2%5Cpi+n%2C+n%5Cin+Z+ "sin^2(\pi-x)+cos( \frac{\pi}{2}+x)=0
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sin^2x-sinx=0
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sinx=0
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x=\pi n, n\in Z
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sinx-1=0
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sinx=1
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x= \frac{\pi}{2}+2\pi n, n\in Z")
