y=x^2-2x 3的极值

f'x(x,y)=e^x(x+2y+y^2+1)=0f'y(x,y)=2e^x(1+y)=0解得x=0y=-1A=f''xx(x,y)=e^x(x+2y+y^2+2)=1B=f''xy(x,y)=2e

对f求x的偏导有：偏导f/偏导x=3x^2-3,令其等于0,解得x=1或者-1再对y求偏导有：偏导f/偏导y=-2y+2,令其等于0,解得y=1.所以极点有：（1,1）或者（-1,1）函数在此点连续,

无极值f(x,y)=x^2y^2-4x^2y-6xy^2+24xy对x求偏导得y(x-3)(y-4)对y求偏导得x(x-6)(y-2)稳定点为{0,0}{0,4}{3,2}{6,4}{6,0}又f对x

y=2x^3-3x^2显然定义域为R,则有y'=6x^2-6x令y'=0则有6x^2-6x=0,解之,得极值点x1=0,x2=1将极值点分别带入方程,得极值y1=0,y2=-1则y'

f(x)=x3+ax2+bxf'=3x^2+2ax+bx=2处有极值-6f'(-2)=3*(-2)^2+2a*(-2)+b=12-4a+b=0.(1)f(-2)=(-2)^3+a*(-2)^2+b=8

由已知得f(x)'=3x^2+4x+1令f(x)'=0则得x=-1或x=-1/3当x＜-1时f(x)'＞0当-1＜x＜-1/3时f(x)'＜0当x＞-1/3时f(x)'＞0所以此函数单调增区间为(-∞

导数的应用.求一阶导3x^2+6ax+3b,x=1处的切线与直线6x+2y+5=0平行,说明斜率是-3.把x=1带入一阶导为-3.在x=2处有极值,说明把x=2带入一阶导为0.

（1）∵函数y=x3+3ax2+3bx+c，∴y'=3x2+6ax+3b，∵函数y=x3+3ax2+3bx+c在x=2处有极值，∴当x=2时，y′=0，即12+12a+3b=0，①∵函数图象在x=1处

函数求导为：3x平方－3＝0令其等于0,得到x1＝1,x2＝－1.当x小于－1时,导数大于0,所以函数递增当x大于－1且小于1时,导数小于0,函数递减当x大于1时,导数大于0,函数递增!且当x＝－1时

f'x=3x^2+3y=0-->y=-x^2f'y=-3y^2+3x=0-->y^2=xx=y^2=x^4-->x=0,1,-->y=0,-1f"xx=6x,f"yy=-6y,f"xy=3f(0,0)

f'x=3x^2-3yf'y=3y^2-3xf'x=0,f'y=0即x^2-y=0y^2-x=0消去yx^4-x=0即x(x-1)(x^2+x+1)=0x=0或1y=0或1x=y=0时f(x,y)=0

f'x=3x^2-3=0,得x=1,-1f'y=-2y+4=0,得y=2f"xx=6x,f"xy=0,f"yy=-2在点(1,2),A=f"xx=6>0,B=f"xy=0,C=f"yy=-2,AC-B

求偏导另其等于0即可

y=x/(x^2+3)y'=[(x^2+3)-x*2x]/(x^2+3)^2=-(x^2-3)/(x^2+3)^2=-(x+√3)(x-√3)/(x^2+3)^2=0x1=-√3,x2=√31.x1=

求偏导对x求偏导得:4-2x对y求偏导得:-4-2y令上面两式等于零得:x=2y=-2所以极值f(x,y)=f(2,-2)=8

对函数求导,y'=3x^2-12x+9求y'=0时的x的值.3x^2-12x+9=0解得x1=1x2=3所以在x等于1和3处取得极值分别代入原函数求的极大值为x1=1时y=0极小值为x2=3时y=-4

y=(x^3-2)/[2(x-1)^2]y'=1/2*[3x^2(x-1)^2-(x^3-2)*2(x-1)]/(x-1)^4=1/2*[3x^2(x-1)-2(x^3-2)]/(x-1)^3=1/2

y'=3x^2-3,令y'=0,x=1或x=-1.当x