![y=(1-x^2)-(x^2-2)^2\\y=1-x^2-(x^4-4x^2+4)\\y=-x^4+3x^2-3\\x^2=a\\y=-a^2+3a-3;\\y=-(a^2-2*3a/2+(3/2)^2-(3/2)^2)-3\\y=-(a-3/2)^2+9/4-3\\y=-(x^2-3/2)^2-3/4\\y=-(x+\sqrt{\frac{3}{2}})^2(x-\sqrt{\frac{3}{2}})^2-0.75\\y'=-2(x+\sqrt{\frac{3}{2}})*(x-\sqrt{\frac{3}{2}})^2-2(x+\sqrt{\frac{3}{2}})^2*(x-\sqrt{\frac{3}{2}})](https://tex.z-dn.net/?f=y%3D%281-x%5E2%29-%28x%5E2-2%29%5E2%5C%5Cy%3D1-x%5E2-%28x%5E4-4x%5E2%2B4%29%5C%5Cy%3D-x%5E4%2B3x%5E2-3%5C%5Cx%5E2%3Da%5C%5Cy%3D-a%5E2%2B3a-3%3B%5C%5Cy%3D-%28a%5E2-2%2A3a%2F2%2B%283%2F2%29%5E2-%283%2F2%29%5E2%29-3%5C%5Cy%3D-%28a-3%2F2%29%5E2%2B9%2F4-3%5C%5Cy%3D-%28x%5E2-3%2F2%29%5E2-3%2F4%5C%5Cy%3D-%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2-0.75%5C%5Cy%27%3D-2%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%2A%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2-2%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2%2A%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29)
Найдём точки экстремумов.
![-2(x+\sqrt{\frac{3}{2}})*(x-\sqrt{\frac{3}{2}})^2-2(x+\sqrt{\frac{3}{2}})^2*(x-\sqrt{\frac{3}{2}})=0\\-2(x+\sqrt{\frac{3}{2}})(x-\sqrt{\frac{3}{2}})((x-\sqrt{\frac{3}{2}})+(x+\sqrt{\frac{3}{2}}))=0\\(x+\sqrt{\frac{3}{2}})(x-\sqrt{\frac{3}{2}})2x=0\\\left[\begin{array}{ccc}x=0\\x=-\sqrt{\frac{3}{2}}\\x=\sqrt{\frac{3}{2}}\end{array}](https://tex.z-dn.net/?f=-2%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%2A%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2-2%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2%2A%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%3D0%5C%5C-2%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%28%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%2B%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%29%3D0%5C%5C%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%292x%3D0%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%3D0%5C%5Cx%3D-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%5C%5Cx%3D%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Cend%7Barray%7D)
Поймём где что, как.
![y'=-4x(x+\sqrt{\frac{3}{2}})(x-\sqrt{\frac{3}{2}})\\x>\sqrt{\frac{3}{2}}\\-*+*+*+=-](https://tex.z-dn.net/?f=y%27%3D-4x%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5C%5Cx%3E%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%5C%5C-%2A%2B%2A%2B%2A%2B%3D-)
Функция убывает.
Возрастает.
Убывает.
Возрастает.
![y=-(x+\sqrt{\frac{3}{2}})^2(x-\sqrt{\frac{3}{2}})^2-0.75](https://tex.z-dn.net/?f=y%3D-%28x%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2%28x-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2-0.75)
Переменная, (+-) что-то в квадрате, значит функция будет расти и убывать достаточно быстро.
Найдём координаты точек экстремума по оси у.
![x=б\sqrt{\frac{3}{2}}\\y=-0.75](https://tex.z-dn.net/?f=x%3D%D0%B1%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%5C%5Cy%3D-0.75)
Точки максимума: ![(-\sqrt{\frac{3}{2}};-0.75)+and+(\sqrt{\frac{3}{2}};-0.75)](https://tex.z-dn.net/?f=%28-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%3B-0.75%29%2Band%2B%28%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%3B-0.75%29)
Найдём координаты точки минимума.
![x=0\\y=-(0+\sqrt{\frac{3}{2}})^2(0-\sqrt{\frac{3}{2}})^2-0.75=\\-\frac{3*3}{2*2}-0.75=\\ -2.25-0.75=-3](https://tex.z-dn.net/?f=x%3D0%5C%5Cy%3D-%280%2B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2%280-%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E2-0.75%3D%5C%5C-%5Cfrac%7B3%2A3%7D%7B2%2A2%7D-0.75%3D%5C%5C+-2.25-0.75%3D-3)
Есть координаты всех точке экстремумов, можем строить.