![y=x* \sqrt{8- x^{2}}](https://tex.z-dn.net/?f=y%3Dx%2A+%5Csqrt%7B8-+x%5E%7B2%7D%7D)
y'=
![\sqrt{8- x^{2}}+ \frac{x*(-2x)}{ \sqrt{8- x^{2}}} = \frac{8- x^{2} -2 x^{2} }{ \sqrt{8- x^{2}}} =](https://tex.z-dn.net/?f=+%5Csqrt%7B8-+x%5E%7B2%7D%7D%2B+%5Cfrac%7Bx%2A%28-2x%29%7D%7B+%5Csqrt%7B8-+x%5E%7B2%7D%7D%7D+%3D+%5Cfrac%7B8-+x%5E%7B2%7D+-2+x%5E%7B2%7D+%7D%7B+%5Csqrt%7B8-+x%5E%7B2%7D%7D%7D++%3D++)
![\frac{8-3 x^{2} }{\sqrt{8- x^{2}}}](https://tex.z-dn.net/?f=%5Cfrac%7B8-3+x%5E%7B2%7D+%7D%7B%5Csqrt%7B8-+x%5E%7B2%7D%7D%7D)
y'=0 =>
![\frac{8-3 x^{2} }{\sqrt{8- x^{2}}}=0 => 8-3 x^{2} =0=> x^{2} = \frac{8}{3} => x1= \frac{2 \sqrt{2} }{ \sqrt{3} } = \frac{2 \sqrt{6} }{3} ; x2=- \frac{2 \sqrt{6} }{3}](https://tex.z-dn.net/?f=%5Cfrac%7B8-3+x%5E%7B2%7D+%7D%7B%5Csqrt%7B8-+x%5E%7B2%7D%7D%7D%3D0+%3D%3E+8-3+x%5E%7B2%7D+%3D0%3D%3E+x%5E%7B2%7D+%3D+%5Cfrac%7B8%7D%7B3%7D+%3D%3E+x1%3D+%5Cfrac%7B2+%5Csqrt%7B2%7D+%7D%7B+%5Csqrt%7B3%7D+%7D+%3D+%5Cfrac%7B2+%5Csqrt%7B6%7D+%7D%7B3%7D+%3B+x2%3D-+%5Cfrac%7B2+%5Csqrt%7B6%7D+%7D%7B3%7D+)
Но:
![8- x^{2}>0 => x^{2} <8 =>](https://tex.z-dn.net/?f=8-+x%5E%7B2%7D%3E0+%3D%3E++x%5E%7B2%7D+%3C8+%3D%3E+)
x∈
![(-2 \sqrt{2} ;2 \sqrt{2})](https://tex.z-dn.net/?f=%28-2+%5Csqrt%7B2%7D+%3B2+%5Csqrt%7B2%7D%29)
При
![-2 \sqrt{2} < x \leq \frac{-2 \sqrt{6} }{3}; y<0](https://tex.z-dn.net/?f=-2+%5Csqrt%7B2%7D+%3C+x+%5Cleq+%5Cfrac%7B-2+%5Csqrt%7B6%7D+%7D%7B3%7D%3B+y%3C0)
(при х=-2 у=-2)
При
![\frac{-2 \sqrt{6} }{3}<span>0](https://tex.z-dn.net/?f=%5Cfrac%7B-2+%5Csqrt%7B6%7D+%7D%7B3%7D%3Cspan%3E0)
(при х=0 у=2
![\sqrt{2}](https://tex.z-dn.net/?f=+%5Csqrt%7B2%7D+)
)
При
![\frac{2 \sqrt{6} }{3} < x \leq 2 \sqrt{2}; y<0](https://tex.z-dn.net/?f=%5Cfrac%7B2+%5Csqrt%7B6%7D+%7D%7B3%7D+%3C+x+%5Cleq+2+%5Csqrt%7B2%7D%3B+y%3C0)
(при х=2 у=-2)
На промежутках, в которых производная функции >0 функция возрастает, где <0 - убывает =>
точки экстремума:
![\frac{-2 \sqrt{6} }{3}](https://tex.z-dn.net/?f=%5Cfrac%7B-2+%5Csqrt%7B6%7D+%7D%7B3%7D)
и
![\frac{2 \sqrt{6} }{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2+%5Csqrt%7B6%7D+%7D%7B3%7D)
Ответ:
а ) 300 - 40 ×2 < ( 300 - 40 ) ×2
б) 54 ÷ ( 3×2) < 54 ÷ 3 ×2
в ) 270 ÷ 9 × 8 = ( 270÷9 ) × 8
г ) 350 ÷ 5 × 2 > 350 ÷ ( 5 × 2 )
300:12=25 парт это 1\12
25*5=125 парт это 5\12 расставили по местам
300- 125=175 парт еще не расставлено