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统计数据
常见 Functions & Graphing 问题
extreme f(x)=5xe^{-4x}
extreme
f
(
x
)
=
5
xe
−
4
x
extreme f(x)=f(x)=5+54x-2x^3,0<= x<= 4
extreme
f
(
x
)
=
f
(
x
)
=
5
+
5
4
x
−
2
x
3
,
0
≤
x
≤
4
extreme f(x)=sqrt(82x^2+180x+100)
extreme
f
(
x
)
=
√
8
2
x
2
+
1
8
0
x
+
1
0
0
extreme P(x,y)=x^2+y^2+16x-16y
extreme
P
(
x
,
y
)
=
x
2
+
y
2
+
1
6
x
−
1
6
y
extreme f(x)=-0.001x^2+9x-1296
extreme
f
(
x
)
=
−
0
.
0
0
1
x
2
+
9
x
−
1
2
9
6
extreme f(x)=((500+500*x))/(1+0.04*x^2)
extreme
f
(
x
)
=
(
5
0
0
+
5
0
0
·
x
)
1
+
0
.
0
4
·
x
2
extreme ((x^2+2))/((x^2-16))
extreme
(
x
2
+
2
)
(
x
2
−
1
6
)
extreme y=2x^2+5
extreme
y
=
2
x
2
+
5
extreme f(x)=5x^4-20x^3+1
extreme
f
(
x
)
=
5
x
4
−
2
0
x
3
+
1
extreme f(x)=0.001x^2+3.2x-10
extreme
f
(
x
)
=
0
.
0
0
1
x
2
+
3
.
2
x
−
1
0
extreme f(x,y)=x^2+y^2-2x-4y
extreme
f
(
x
,
y
)
=
x
2
+
y
2
−
2
x
−
4
y
extreme f(x)=-7x^2-7xy-6y^2-35x-26y+9
extreme
f
(
x
)
=
−
7
x
2
−
7
xy
−
6
y
2
−
3
5
x
−
2
6
y
+
9
extreme 3(x-4)^{2/3}+6
extreme
3
(
x
−
4
)
2
3
+
6
extreme y=x^3+3x^2
extreme
y
=
x
3
+
3
x
2
extreme f(x)=4x^{3/5}
extreme
f
(
x
)
=
4
x
3
5
extreme f(x)=x-(x/y)*y
extreme
f
(
x
)
=
x
−
(
x
y
)
·
y
extreme f(x)=6x^3+27x^2-180x
extreme
f
(
x
)
=
6
x
3
+
2
7
x
2
−
1
8
0
x
extreme f(x)=(5-x)5^x
extreme
f
(
x
)
=
(
5
−
x
)
5
x
extreme f(x)=-4\sqrt[4]{x^2+y^2+81}
extreme
f
(
x
)
=
−
4
4
√
x
2
+
y
2
+
8
1
extreme 2x^3-33x^2+108x+5
extreme
2
x
3
−
3
3
x
2
+
1
0
8
x
+
5
extreme f(x)=x^3-3/2 x^2,-2<= x<= 4
extreme
f
(
x
)
=
x
3
−
3
2
x
2
,
−
2
≤
x
≤
4
extreme x^3-6x^2+2x-2
extreme
x
3
−
6
x
2
+
2
x
−
2
extreme f(x)=x+4/x ,1<= x<= 10
extreme
f
(
x
)
=
x
+
4
x
,
1
≤
x
≤
1
0
extreme 2θ-3sin(θ)
extreme
2
θ
−
3
sin
(
θ
)
extreme f(x)=x^2+2x-30
extreme
f
(
x
)
=
x
2
+
2
x
−
3
0
extreme-1/(x^2+49)-1/((x-5)^2+4)
extreme
−
1
x
2
+
4
9
−
1
(
x
−
5
)
2
+
4
extreme f(x)=x*(ln(x))^2
extreme
f
(
x
)
=
x
·
(
ln
(
x
)
)
2
extreme f(x)=x[36-2(x)]^2
extreme
f
(
x
)
=
x
[
3
6
−
2
(
x
)
]
2
extreme f(x)=sqrt(x+12)-8
extreme
f
(
x
)
=
√
x
+
1
2
−
8
extreme f(x,y)=4xy+120y-20y^2-1/10 x^2y-90
extreme
f
(
x
,
y
)
=
4
xy
+
1
2
0
y
−
2
0
y
2
−
1
1
0
x
2
y
−
9
0
extreme f(x,y)=2x^2+4y^2-2xy-10x-2y+2
extreme
f
(
x
,
y
)
=
2
x
2
+
4
y
2
−
2
xy
−
1
0
x
−
2
y
+
2
extreme f(x)=(7x)/(x^2+9),0<= x<= 9
extreme
f
(
x
)
=
7
x
x
2
+
9
,
0
≤
x
≤
9
extreme 2x^3+4x^2-1
extreme
2
x
3
+
4
x
2
−
1
extreme f(x)=x*(ln(x))^5
extreme
f
(
x
)
=
x
·
(
ln
(
x
)
)
5
extreme f(x,y)=40000x+30000y-8x^2-15y^2-10xy
extreme
f
(
x
,
y
)
=
4
0
0
0
0
x
+
3
0
0
0
0
y
−
8
x
2
−
1
5
y
2
−
1
0
xy
extreme f(x)=e^{x^3-3x}
extreme
f
(
x
)
=
e
x
3
−
3
x
extreme f(x)=x+(30)/x
extreme
f
(
x
)
=
x
+
3
0
x
extreme (5x+4)/(x+sqrt(x))
extreme
5
x
+
4
x
+
√
x
extreme F(x,y)=x*y+(pi*(x/2)^2)/2
extreme
F
(
x
,
y
)
=
x
·
y
+
π
·
(
x
2
)
2
2
extreme f(x)=-(5x^4)/4-(4x^3)/3-4
extreme
f
(
x
)
=
−
5
x
4
4
−
4
x
3
3
−
4
extreme f(x)=4(z^{-x})+1
extreme
f
(
x
)
=
4
(
z
−
x
)
+
1
extreme y=15xe^{-x}
extreme
y
=
1
5
xe
−
x
extreme f(x)=x^2+6
extreme
f
(
x
)
=
x
2
+
6
extreme f(x)=6sqrt(x^2+1)-x,0<= x<= 3
extreme
f
(
x
)
=
6
√
x
2
+
1
−
x
,
0
≤
x
≤
3
extreme f(x)=x^2-x-5
extreme
f
(
x
)
=
x
2
−
x
−
5
extreme 5x^3+67.5x^2+2x+10
extreme
5
x
3
+
6
7
.
5
x
2
+
2
x
+
1
0
extreme f(x)=25x^2-x^3
extreme
f
(
x
)
=
2
5
x
2
−
x
3
extreme f(x)=4x^2-16x+20
extreme
f
(
x
)
=
4
x
2
−
1
6
x
+
2
0
extreme g(x)=-50x^2+400x+500
extreme
g
(
x
)
=
−
5
0
x
2
+
4
0
0
x
+
5
0
0
extreme f(x)=4x+5y
extreme
f
(
x
)
=
4
x
+
5
y
extreme x^{11}-3x^9+2
extreme
x
1
1
−
3
x
9
+
2
extreme x^3-2x^2-4x-4
extreme
x
3
−
2
x
2
−
4
x
−
4
extreme 9x^3-7x^2+3x+10
extreme
9
x
3
−
7
x
2
+
3
x
+
1
0
extreme f(x)=4+27x-x^3
extreme
f
(
x
)
=
4
+
2
7
x
−
x
3
extreme f(x)=-(8x)/((x^2+1)^2)
extreme
f
(
x
)
=
−
8
x
(
x
2
+
1
)
2
extreme f(x)= x/((1+x)^2)
extreme
f
(
x
)
=
x
(
1
+
x
)
2
extreme y=x^2-4x+19
extreme
y
=
x
2
−
4
x
+
1
9
extreme f(x)=-6e^{-x^2}
extreme
f
(
x
)
=
−
6
e
−
x
2
extreme-16x+56y-x^2+4xy-6y^2+6
extreme
−
1
6
x
+
5
6
y
−
x
2
+
4
xy
−
6
y
2
+
6
extreme y=x^2+10x+21
extreme
y
=
x
2
+
1
0
x
+
2
1
extreme f(x)=189x-(x^2)/(354)
extreme
f
(
x
)
=
1
8
9
x
−
x
2
3
5
4
extreme y=x^3+6x-6
extreme
y
=
x
3
+
6
x
−
6
extreme 6xye^{-x^2-y^2}
extreme
6
xye
−
x
2
−
y
2
extreme-x+2cos(x),0<= x<= 2pi
extreme
−
x
+
2
cos
(
x
)
,
0
≤
x
≤
2
π
extreme f(x)=(4x^2)/(3+x)
extreme
f
(
x
)
=
4
x
2
3
+
x
extreme 125x^3-15x+1
extreme
1
2
5
x
3
−
1
5
x
+
1
extreme f(x)=x^2+xy+2x+2y+3
extreme
f
(
x
)
=
x
2
+
xy
+
2
x
+
2
y
+
3
extreme f(x)=x(e^x)
extreme
f
(
x
)
=
x
(
e
x
)
extreme f(x,y)=2x^2+2y^2-x^4-y^4+3
extreme
f
(
x
,
y
)
=
2
x
2
+
2
y
2
−
x
4
−
y
4
+
3
extreme sin(2x)+cos(2x)
extreme
sin
(
2
x
)
+
cos
(
2
x
)
extreme f(x)= x/((x^2+4))
extreme
f
(
x
)
=
x
(
x
2
+
4
)
extreme f(x)=-0.5x^2
extreme
f
(
x
)
=
−
0
.
5
x
2
extreme f(x)=5xe^{-5x}
extreme
f
(
x
)
=
5
xe
−
5
x
extreme y=x^3-3x^2-9x
extreme
y
=
x
3
−
3
x
2
−
9
x
extreme f(x)=xe^{-2x^2-2y^2}
extreme
f
(
x
)
=
xe
−
2
x
2
−
2
y
2
extreme f(z)=z+z^3-2z^2-4
extreme
f
(
z
)
=
z
+
z
3
−
2
z
2
−
4
extreme f(x)=1+1/x+5/(x^2)+1/(x^3)
extreme
f
(
x
)
=
1
+
1
x
+
5
x
2
+
1
x
3
extreme f(x)=(x^2-0.8x+0.32)/(1.6-2x)
extreme
f
(
x
)
=
x
2
−
0
.
8
x
+
0
.
3
2
1
.
6
−
2
x
extreme f(x)=3x^2-9x+9xy^2
extreme
f
(
x
)
=
3
x
2
−
9
x
+
9
xy
2
extreme f(x)=|(x-2)/(x+5)|-3
extreme
f
(
x
)
=
|
x
−
2
x
+
5
|
−
3
extreme 2x^4-x^2+5
extreme
2
x
4
−
x
2
+
5
extreme f(x)=7x^9-9x^7-5(-3.4)
extreme
f
(
x
)
=
7
x
9
−
9
x
7
−
5
(
−
3
.
4
)
extreme f(x)=-3+x^2-3x-3x^3+2x^5+4x^4
extreme
f
(
x
)
=
−
3
+
x
2
−
3
x
−
3
x
3
+
2
x
5
+
4
x
4
extreme f(x)=-x^3+6x^2+135x+1
extreme
f
(
x
)
=
−
x
3
+
6
x
2
+
1
3
5
x
+
1
extreme x^2-8x+15
extreme
x
2
−
8
x
+
1
5
extreme x^2-8x+13
extreme
x
2
−
8
x
+
1
3
extreme f(x)=2x^2-5x+2
extreme
f
(
x
)
=
2
x
2
−
5
x
+
2
extreme f(x)= x/(ln(x))[2.1]
extreme
f
(
x
)
=
x
ln
(
x
)
[
2
.
1
]
extreme f(x)=x^4-72x^2-2,-7<= x<= 7
extreme
f
(
x
)
=
x
4
−
7
2
x
2
−
2
,
−
7
≤
x
≤
7
extreme f(x)=x^2+10x^{2/3}
extreme
f
(
x
)
=
x
2
+
1
0
x
2
3
extreme y=-x^2+1-,1<= x<= 2
extreme
y
=
−
x
2
+
1
−
,
1
≤
x
≤
2
extreme f(x)=3x^4-12x^3-60x^2+4
extreme
f
(
x
)
=
3
x
4
−
1
2
x
3
−
6
0
x
2
+
4
extreme f(x)=13e^{-x}
extreme
f
(
x
)
=
1
3
e
−
x
extreme f(x)=-x^4-6x
extreme
f
(
x
)
=
−
x
4
−
6
x
extreme P(X,Y)=36X^2-9Y^2
extreme
P
(
X
,
Y
)
=
3
6
X
2
−
9
Y
2
extreme f(x)=9x^2-2
extreme
f
(
x
)
=
9
x
2
−
2
extreme 4/(sqrt(x))
extreme
4
√
x
extreme f(x)=-4x^2+40x-60
extreme
f
(
x
)
=
−
4
x
2
+
4
0
x
−
6
0
extreme 1/(x^2+2x-8)
extreme
1
x
2
+
2
x
−
8
extreme f(x)=9x^2+3
extreme
f
(
x
)
=
9
x
2
+
3
1
..
828
829
830
831
832
..
839
