已知x??+y??=1,求(x-y)??的最大值
=x??-2xy+y??=(sint)??+(cost)??-2sintcost=1-sin2t即:(x-y)??的最大值=1*[1-(-1)]=2。思路三:判别式法设x-y=t,则y=x-t,代入已知条件得:x??+(x-t)??=1x??+x??-2xt+t??-1=02x??-2xt+t??-1=0,把方程看成x的二次方程,则:判别式△=4t...
当z=f(3xy,x^2+y^2,x^3),求z对x,y的所有二阶偏导数
z=f(3xy,x^2+y^2,x^3),用全微分求导法,则有:dz=3f1'(ydx+xdy)+f2'(2xdx+2ydy)+3x^2f3'dx,即:dz=3yf1'dx+3xf1'dy+2xf2'dx+2yf2'dy+3x^2f3'dx,dz=(3yf1'+2xf2'+3x^2f3')dx+(3xf1'+2yf2')dy。则z对x的一阶偏导数为:??z/??x=3yf1'+2xf2'+3x^2f3';同...
z=x^3y^2-xy^3+xy+1的所有一二三阶偏导数
dz/dy=x^3*2y-x*3y^2+x=2yx^3-3xy^2+x。二阶偏导数:∵dz/dx=3x^2y^2-y^3+y,∴d^2z/dx^2=3y^2*2x-0+0=6xy^2,d^2z/dxdy=3x^2*2y-3y^2+1=6yx^2-3y^2+1;∵dz/dy=2yx^3-3xy^2+x,∴d^2z/dy^2=2x^3x*2y+0=2x^3-6xy,d^2z/dydx=2y*3x^2-...
已知27x^3+y^3=1,求3x+y的最大值
3.y=x^(1/3),则其导数y’=(1/3)x^(-2/3)。二次函数判别式法:27x^3+y^3=(3x+y)(9x^2-3xy+y^2)=(3x+y)[(3x+y)^2-9xy]设3x+y=k,则:1=k(k^2-9xy),即:3x*1y=(1/3)(k^2-1/k),3x和1y可以看成如下t的二次方程的两个根:t^2-kt+(1/3)(k^2-1/...
实数x,y有x^2-4xy+20y^2=3,求x+y的取值范围
2x-4(y+xy')+40yy'=02x-4y+(40y-4x)y'=0,将y'=-1代入有:2x-4y-(40y-4x)=0,即3x=22y,代入已知方程中,有:(22y/3)^2-4*(22y*y/3)+20y^2=3所以y^2=3*9/400,则:y=±3√3/20,所以x+y的最大值=(22/3+1)*3√3/20=5√3/4,...