Dz/dx=2x-5y-5 d^2z/dx^2=2=А
dz/dy=-5x-4y+4 d^2z/dy^2=-4=B
d^2z/dxdy=-5=C
2x-5y=5 10x-25y=25
5x+4y=4 10x+8y=8
-33y=17
y=-17/33
x=40/33
A=2>0 B=-4 C=-5
AC-B^2=<0 нет экстремума
Вариант 1
1. а) =(4-x)² /(x-4) =(x-4)²/(x-4) =x -4
b) =x²(x^3 -3) /2x^4(x^3 -3) =1/2x²
в) x^4 -2x²y² +y^4 =(x² -y²)² =(x²-y²)(x²-y²) =(x-y)(x+y)(x-y)(x+y) =(x-y)²(x+y)²
=7y²(x²-2xy+y²) /(x-y)²(x+y)² =7y²(x -y)² /(x-y)²(x+y)² =7y² /(x+y)²
вариант 2
1. а) =(5-x)² /(x-5) =(x-5)² /(x-5) =x -5
b) =x²(3x²+2) /5x^6(3x²+2) =1/5x^4
в) =(x²-y²)² / (12x^3y +12x²y²) =(x-y)²(x+y)² / 12x²y(x+y)=(x+y)(x-y)² /12x²y