![z=-6x^2+y^2-9xy+12](https://tex.z-dn.net/?f=z%3D-6x%5E2%2By%5E2-9xy%2B12)
І. Находим частные производные первого порядка
![z'_{x}=-12x-9y;\\ z'_{y}=2y-9x;](https://tex.z-dn.net/?f=z%27_%7Bx%7D%3D-12x-9y%3B%5C%5C+z%27_%7By%7D%3D2y-9x%3B)
ІІ. Ищем критические точки
![z'_{x}=0; z'_{y}=0;](https://tex.z-dn.net/?f=z%27_%7Bx%7D%3D0%3B+z%27_%7By%7D%3D0%3B)
![-12x-9y=0;\\ 2y-9x=0;](https://tex.z-dn.net/?f=-12x-9y%3D0%3B%5C%5C+2y-9x%3D0%3B)
![4x+3y=0;\\ y=4.5x;](https://tex.z-dn.net/?f=4x%2B3y%3D0%3B%5C%5C+y%3D4.5x%3B+)
![4x-3*4.5x=0;\\ y=4.5x](https://tex.z-dn.net/?f=4x-3%2A4.5x%3D0%3B%5C%5C+y%3D4.5x+)
M(0;0)- критическая точка
III. Ищем вторые производные
![z^{''}_{x^2}=-12;\\ z^{''}_{xy}=-9;\\ z^{''}_{y^2}=2](https://tex.z-dn.net/?f=z%5E%7B%27%27%7D_%7Bx%5E2%7D%3D-12%3B%5C%5C+z%5E%7B%27%27%7D_%7Bxy%7D%3D-9%3B%5C%5C+z%5E%7B%27%27%7D_%7By%5E2%7D%3D2)
IV. Находим значение вторых производных в критической точке
![z^{''}_{x^2} (M)=-12;\\ z^{''}_{xy}(M)=-9;\\ z^{''}_{y^2}(M)=2;\\ A=-12; B=-9 ; C=2;\\ A<0; \Delta=AC-B^2=-12*2-(-9)^2=-24-81=-105<0;](https://tex.z-dn.net/?f=z%5E%7B%27%27%7D_%7Bx%5E2%7D+%28M%29%3D-12%3B%5C%5C+z%5E%7B%27%27%7D_%7Bxy%7D%28M%29%3D-9%3B%5C%5C+z%5E%7B%27%27%7D_%7By%5E2%7D%28M%29%3D2%3B%5C%5C+A%3D-12%3B+B%3D-9+%3B+C%3D2%3B%5C%5C+A%3C0%3B+%5CDelta%3DAC-B%5E2%3D-12%2A2-%28-9%29%5E2%3D-24-81%3D-105%3C0%3B)
следовательно в точке М экстремумов нет
ответ: данная функция экстремум не имеет
1 число существует (сорок шесть) поэтому ответ б)1
это можно решить крест накрест итого 200*270/180=300 и всё
15/(a - b) · (b - a)/10 = 15(b - a)/(a - b)10 = 3(-a + b)/(a - b)2 = (-3)(a - b)/(a - b)2 = (-3)/ /2 = (-1,5)
(-a - b/a)² = a² - (a · 2 · b/a) + (b/a)² = a²/1 - (2ab/a) + (b²/a²) = a⁴/a² - 2ba²/a² + b²/ /a² = (a⁴ - 2a²b + b²)/a²
3/(a - b)² ÷ (-3)/(a - b) = 3/(a - b)(a - b) · (a - b)/(-3) = 3(a - b)/(a - b)(a - b)(-3) = 1/(-1)(a -- b) =1/((-a) + b) = 1/(b - a)
1/(a + b) ÷ 1/3x(a + b) = 1/(a + b) · 3x(a + b)/1 = 3x(a + b)/(a + b) = 3x
(2/b)² · (b/4)² = 2²/b² · b²/4² = 4/b² · b²/16 = 4b²/16b² = 1/4
(9 - y²)/(3 - y) · y/(y² + 6y + 9) = (3 - y)(3 + y)/(3 - y) · y/(y + 3)² = y(3 - y)(y + 3)/(3 - y)(y + 3)(y + 3) = y/(y + 3)
(x² + 5x)/(x² - 4) ÷ (x² + 10 + 25)/(x + 2) · (x + 5)/x = x(x + 5)/(x - 2)(x + 2) ÷ (x + 5)²/
/(x + 2) · (x + 5)/x = x(x + 5)/(x - 2)(x + 2) · (x + 2)/(x + 5)(x + 5) · (x + 5)/x = x(x + 5)(x + + 2)(x + 5)/(x - 2)(x + 2)(x + 5)(x + 5)x = 1/(x - 2)
(1 - (x/y)²) ÷ (1/x - 1/y) = (1 - (x²/y²)) ÷ (y/xy - x/xy) = (y²/y² - x²/y²) ÷ (y - x)/xy = (y² - x²)/ /y² · xy/(x - y) = (y - x)xy²/y²(x - y) = (-(x - y))xy²/y²(x - y) = (-x)