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统计数据
常见 Functions & Graphing 问题
extreme f(x,y)=x^4-2x^2+y^3-3y
extreme
f
(
x
,
y
)
=
x
4
−
2
x
2
+
y
3
−
3
y
extreme ln(x^4+27)
extreme
ln
(
x
4
+
2
7
)
extreme f(x,y)=(2y-x)/((x-1)^2+(y-2)^2)
extreme
f
(
x
,
y
)
=
2
y
−
x
(
x
−
1
)
2
+
(
y
−
2
)
2
extreme f(x,y)=sqrt(x-1)sqrt(y-1)
extreme
f
(
x
,
y
)
=
√
x
−
1
√
y
−
1
extreme f(x,y)=8x^3+2xy-3x^2+y^2+1
extreme
f
(
x
,
y
)
=
8
x
3
+
2
xy
−
3
x
2
+
y
2
+
1
extreme f(x)=3x+4y
extreme
f
(
x
)
=
3
x
+
4
y
extreme f(x)=3x^2-18x+24
extreme
f
(
x
)
=
3
x
2
−
1
8
x
+
2
4
extreme f(x,y)=-2x^2-2y^2-4xy+5x+4y
extreme
f
(
x
,
y
)
=
−
2
x
2
−
2
y
2
−
4
xy
+
5
x
+
4
y
extreme f(x)=(x^2+x)^{2/3}
extreme
f
(
x
)
=
(
x
2
+
x
)
2
3
extreme f(xy)=x^3+y^3+2x^2+4y^2+6
extreme
f
(
xy
)
=
x
3
+
y
3
+
2
x
2
+
4
y
2
+
6
extreme f(x)= 1/2 x^3-3xy+3y^2-x
extreme
f
(
x
)
=
1
2
x
3
−
3
xy
+
3
y
2
−
x
extreme (x^2)/((x-1)^2)
extreme
x
2
(
x
−
1
)
2
extreme f(x,y)=-3x^2+7xy-4y^2+x+y
extreme
f
(
x
,
y
)
=
−
3
x
2
+
7
xy
−
4
y
2
+
x
+
y
extreme f(x)=x^3-27x+7
extreme
f
(
x
)
=
x
3
−
2
7
x
+
7
extreme f(x)= 10/3 x^3-11x^2+12x-24
extreme
f
(
x
)
=
1
0
3
x
3
−
1
1
x
2
+
1
2
x
−
2
4
extreme x/(sqrt(x^2+1))
extreme
x
√
x
2
+
1
extreme f(x,y)=x^3+y^2-2xy-x+3
extreme
f
(
x
,
y
)
=
x
3
+
y
2
−
2
xy
−
x
+
3
extreme f(x)=5x-60x^{1/3}
extreme
f
(
x
)
=
5
x
−
6
0
x
1
3
extreme f(x)= 1/6 (x^3-6x^2+9x+6)
extreme
f
(
x
)
=
1
6
(
x
3
−
6
x
2
+
9
x
+
6
)
extreme f(x,y)=x^2-3xy+y^2
extreme
f
(
x
,
y
)
=
x
2
−
3
xy
+
y
2
extreme 16
extreme
1
6
extreme f(x)=-5+y-10x
extreme
f
(
x
)
=
−
5
+
y
−
1
0
x
extreme f(x)=4x^3-12x^2+9x-1
extreme
f
(
x
)
=
4
x
3
−
1
2
x
2
+
9
x
−
1
extreme y=2xz
extreme
y
=
2
xz
extreme f(x)=x^9-9x
extreme
f
(
x
)
=
x
9
−
9
x
extreme f(x)=x^2(x-2)^3(x+2)^3
extreme
f
(
x
)
=
x
2
(
x
−
2
)
3
(
x
+
2
)
3
extreme f(x)=2x^5-6x^4
extreme
f
(
x
)
=
2
x
5
−
6
x
4
extreme f(x)=-(x^2+x)^{2/3}
extreme
f
(
x
)
=
−
(
x
2
+
x
)
2
3
extreme f(x)=(x^3)/(x^3+1)
extreme
f
(
x
)
=
x
3
x
3
+
1
extreme f(x)=98y^2+x^2-x^2y
extreme
f
(
x
)
=
9
8
y
2
+
x
2
−
x
2
y
extreme f(x)=((x+4)(x-3)^2)/(x^4(x-1))
extreme
f
(
x
)
=
(
x
+
4
)
(
x
−
3
)
2
x
4
(
x
−
1
)
extreme f(x)=x(6-2x)^2
extreme
f
(
x
)
=
x
(
6
−
2
x
)
2
extreme f(x)= 1/4 x^4+1/3 x^3-x^2+2/3
extreme
f
(
x
)
=
1
4
x
4
+
1
3
x
3
−
x
2
+
2
3
extreme f(x,y)=-4*(x^2+6x+8)/(y^2+6y+6)
extreme
f
(
x
,
y
)
=
−
4
·
x
2
+
6
x
+
8
y
2
+
6
y
+
6
extreme f(x)=x+(108)/(x^2)
extreme
f
(
x
)
=
x
+
1
0
8
x
2
extreme f(x)=(3x^2)/(1/2 x^2+1)
extreme
f
(
x
)
=
3
x
2
1
2
x
2
+
1
extreme g(x,y)=xy^{1/2}
extreme
g
(
x
,
y
)
=
xy
1
2
extreme f(x)=x^3-6x^2+12x-5
extreme
f
(
x
)
=
x
3
−
6
x
2
+
1
2
x
−
5
extreme f(x,y)=x^4-4x^2+y^4-8y^2+5
extreme
f
(
x
,
y
)
=
x
4
−
4
x
2
+
y
4
−
8
y
2
+
5
extreme x^3-6x^2+9x+5
extreme
x
3
−
6
x
2
+
9
x
+
5
extreme f(x)=x^4-4x^3-8x^2+8
extreme
f
(
x
)
=
x
4
−
4
x
3
−
8
x
2
+
8
extreme f(x,y)=6-x-2y
extreme
f
(
x
,
y
)
=
6
−
x
−
2
y
extreme (x^3)/3-2x^2+3x
extreme
x
3
3
−
2
x
2
+
3
x
extreme (-3x+45)/((x-95)^{11)}
extreme
−
3
x
+
4
5
(
x
−
9
5
)
1
1
extreme f(x)=ln(x+1)
extreme
f
(
x
)
=
ln
(
x
+
1
)
extreme f(x,y)=ln(x^2+y^2-9)
extreme
f
(
x
,
y
)
=
ln
(
x
2
+
y
2
−
9
)
extreme 4x^2y+2xy^2-12xy-5
extreme
4
x
2
y
+
2
xy
2
−
1
2
xy
−
5
extreme K(r,s)=4r-s
extreme
K
(
r
,
s
)
=
4
r
−
s
extreme f(x)=3x^4+4x^3-12x^2+2
extreme
f
(
x
)
=
3
x
4
+
4
x
3
−
1
2
x
2
+
2
extreme f(x)=3x^4+4x^3-12x^2+7
extreme
f
(
x
)
=
3
x
4
+
4
x
3
−
1
2
x
2
+
7
extreme f(x,y)=2xy-2x^2-y^3+3
extreme
f
(
x
,
y
)
=
2
xy
−
2
x
2
−
y
3
+
3
extreme f(x,y)=xye^{(-x-y)}
extreme
f
(
x
,
y
)
=
xye
(
−
x
−
y
)
extreme x^2-6x+5
extreme
x
2
−
6
x
+
5
extreme x/(x+3)
extreme
x
x
+
3
extreme f(x)=(4x-2)/(x^2-10x+25)
extreme
f
(
x
)
=
4
x
−
2
x
2
−
1
0
x
+
2
5
extreme f(x,y)=xy+5x-5
extreme
f
(
x
,
y
)
=
xy
+
5
x
−
5
extreme f(x,y)=x^2+2xy+2y^2-x+2y
extreme
f
(
x
,
y
)
=
x
2
+
2
xy
+
2
y
2
−
x
+
2
y
extreme f(x)=x-1/6 x^2-2/3 ln(x)
extreme
f
(
x
)
=
x
−
1
6
x
2
−
2
3
ln
(
x
)
extreme y=x^3-6x^2+9x-8
extreme
y
=
x
3
−
6
x
2
+
9
x
−
8
extreme f(x)=12+2x-x^2
extreme
f
(
x
)
=
1
2
+
2
x
−
x
2
extreme f(x)=(x^2-24)/(x-5)
extreme
f
(
x
)
=
x
2
−
2
4
x
−
5
extreme f(x)=ln(x)-x
extreme
f
(
x
)
=
ln
(
x
)
−
x
extreme f(x)=(4x)/(x^2+25)
extreme
f
(
x
)
=
4
x
x
2
+
2
5
extreme y=x^2-3x
extreme
y
=
x
2
−
3
x
extreme f(x,y)=x^2+y^4+2xy
extreme
f
(
x
,
y
)
=
x
2
+
y
4
+
2
xy
extreme f(x,y)=x^4+y^4-4xy+4
extreme
f
(
x
,
y
)
=
x
4
+
y
4
−
4
xy
+
4
extreme f(x)=x^3-12x-10
extreme
f
(
x
)
=
x
3
−
1
2
x
−
1
0
extreme g(x)=x^2-6x-12
extreme
g
(
x
)
=
x
2
−
6
x
−
1
2
extreme f(x)=(x^3-5x^2+11x-11)e^x
extreme
f
(
x
)
=
(
x
3
−
5
x
2
+
1
1
x
−
1
1
)
e
x
extreme f(x)=5x+3/x
extreme
f
(
x
)
=
5
x
+
3
x
extreme f(x)=-x^2+6x-4
extreme
f
(
x
)
=
−
x
2
+
6
x
−
4
extreme f(x)=x^2-12x+7
extreme
f
(
x
)
=
x
2
−
1
2
x
+
7
extreme f(x)=-x^3+3x^2+5
extreme
f
(
x
)
=
−
x
3
+
3
x
2
+
5
extreme (6x^2)/(x^2-16)
extreme
6
x
2
x
2
−
1
6
extreme f(x,y)=x^2-y^2+6x-8y+25
extreme
f
(
x
,
y
)
=
x
2
−
y
2
+
6
x
−
8
y
+
2
5
extreme f(x,y)=x+4y
extreme
f
(
x
,
y
)
=
x
+
4
y
extreme f(x)=x^4+y^4-4x^2y+2y
extreme
f
(
x
)
=
x
4
+
y
4
−
4
x
2
y
+
2
y
extreme (x^2-24)/(x-5)
extreme
x
2
−
2
4
x
−
5
extreme f(x)=2x^3-3x^2+1
extreme
f
(
x
)
=
2
x
3
−
3
x
2
+
1
extreme f(x,y)=20x+64y+8xy-x^2-32y^2
extreme
f
(
x
,
y
)
=
2
0
x
+
6
4
y
+
8
xy
−
x
2
−
3
2
y
2
extreme (x^2-1)/(x^2-4)
extreme
x
2
−
1
x
2
−
4
extreme f(x)=5x^2ln(x)
extreme
f
(
x
)
=
5
x
2
ln
(
x
)
extreme f(x,y)=2x^2+8xy+y^4
extreme
f
(
x
,
y
)
=
2
x
2
+
8
xy
+
y
4
F(m,a)=m*a
F
(
m
,
a
)
=
m
·
a
extreme f(x,y)=x^3+y^3-3x-3y+20
extreme
f
(
x
,
y
)
=
x
3
+
y
3
−
3
x
−
3
y
+
2
0
extreme f(x,y)=x^3+y^2-4xy+17x-10y+8
extreme
f
(
x
,
y
)
=
x
3
+
y
2
−
4
xy
+
1
7
x
−
1
0
y
+
8
extreme f(x)=2x^3+45x^2+84x+29
extreme
f
(
x
)
=
2
x
3
+
4
5
x
2
+
8
4
x
+
2
9
extreme f(x,y)= 1/3 y^3+x^2-2xy-15y+12
extreme
f
(
x
,
y
)
=
1
3
y
3
+
x
2
−
2
xy
−
1
5
y
+
1
2
extreme f(x,y)=3xy^2-x^3-15x+36y+9
extreme
f
(
x
,
y
)
=
3
xy
2
−
x
3
−
1
5
x
+
3
6
y
+
9
extreme f(x)=2x^3-3ax^2+a^3
extreme
f
(
x
)
=
2
x
3
−
3
ax
2
+
a
3
extreme f(x)=x(x-3)^2(x+1)
extreme
f
(
x
)
=
x
(
x
−
3
)
2
(
x
+
1
)
extreme f(x)=-4x^2-32x-62
extreme
f
(
x
)
=
−
4
x
2
−
3
2
x
−
6
2
extreme f(x,y)=2x^3+6xy^2-3y^3-150x
extreme
f
(
x
,
y
)
=
2
x
3
+
6
xy
2
−
3
y
3
−
1
5
0
x
extreme (x-2)^2+1
extreme
(
x
−
2
)
2
+
1
extreme f(x)=sin(x),0<= x< pi/2
extreme
f
(
x
)
=
sin
(
x
)
,
0
≤
x
<
π
2
extreme f(x)=(x^2-4)^2-4
extreme
f
(
x
)
=
(
x
2
−
4
)
2
−
4
extreme f(x)= 2/3 x^3-4x^2-45x
extreme
f
(
x
)
=
2
3
x
3
−
4
x
2
−
4
5
x
extreme f(x,y)=x^2+xy+y^2-37y+456
extreme
f
(
x
,
y
)
=
x
2
+
xy
+
y
2
−
3
7
y
+
4
5
6
extreme f(x,y)=3x^2-y^2
extreme
f
(
x
,
y
)
=
3
x
2
−
y
2
extreme 3x^5-5x^3+1
extreme
3
x
5
−
5
x
3
+
1
1
..
549
550
551
552
553
..
839
