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常见 Functions & Graphing 问题
critical 2x^3+3x^2-12x-7
critical
2
x
3
+
3
x
2
−
1
2
x
−
7
critical f(x)=(x^3+2x+3)/(x^4+4x^2+4)
critical
f
(
x
)
=
x
3
+
2
x
+
3
x
4
+
4
x
2
+
4
critical f(x)=-1/((x-1)^2)
critical
f
(
x
)
=
−
1
(
x
−
1
)
2
critical f(x,y)=x^2+y^2-2x-2y+3
critical
f
(
x
,
y
)
=
x
2
+
y
2
−
2
x
−
2
y
+
3
critical f(x)=1-sin(x)
critical
f
(
x
)
=
1
−
sin
(
x
)
critical f(x)=((3x-2))/(x^2-2x+1)
critical
f
(
x
)
=
(
3
x
−
2
)
x
2
−
2
x
+
1
critical f(x)=-e^{-2x^2-1}x
critical
f
(
x
)
=
−
e
−
2
x
2
−
1
x
critical f(x)=x^4-2x^3+3
critical
f
(
x
)
=
x
4
−
2
x
3
+
3
critical f(x)= 1/4 x^2-2x^2
critical
f
(
x
)
=
1
4
x
2
−
2
x
2
critical x^3-4x^2-3x+2
critical
x
3
−
4
x
2
−
3
x
+
2
critical h(x)=ln(x^3)-9x
critical
h
(
x
)
=
ln
(
x
3
)
−
9
x
critical f(x)=x^2-x-1
critical
f
(
x
)
=
x
2
−
x
−
1
critical f(x)=(x^3)/3-ln(x)
critical
f
(
x
)
=
x
3
3
−
ln
(
x
)
critical y=(x^2+2)/(2x-1)
critical
y
=
x
2
+
2
2
x
−
1
critical f(x)=x^3+9x^2+b
critical
f
(
x
)
=
x
3
+
9
x
2
+
b
critical x^{8/3}-8x^{1/3}
critical
x
8
3
−
8
x
1
3
critical f(x)=x^3+3x^2y-3xy^2+y^3
critical
f
(
x
)
=
x
3
+
3
x
2
y
−
3
xy
2
+
y
3
critical e^{-x}x^2+e^{-x}
critical
e
−
x
x
2
+
e
−
x
critical f(x)=3x+2/x+6
critical
f
(
x
)
=
3
x
+
2
x
+
6
critical-csc^2(x)
critical
−
csc
2
(
x
)
critical f(x)=9x^2+2x^3
critical
f
(
x
)
=
9
x
2
+
2
x
3
critical f(x)=e^{x^2-6x-1}
critical
f
(
x
)
=
e
x
2
−
6
x
−
1
critical (x^2-2x+1)/(x+1)
critical
x
2
−
2
x
+
1
x
+
1
critical x^3e^{-8x}
critical
x
3
e
−
8
x
critical f(x)=(x-7)^4(x+6)^5
critical
f
(
x
)
=
(
x
−
7
)
4
(
x
+
6
)
5
critical f(x)=\sqrt[3]{1-x^2}
critical
f
(
x
)
=
3
√
1
−
x
2
critical f(x)=(x-4)e^{-3x}
critical
f
(
x
)
=
(
x
−
4
)
e
−
3
x
critical f(x)=|sin(x)|,0<x<2pi
critical
f
(
x
)
=
|
sin
(
x
)
|
,
0
<
x
<
2
π
critical (2x^2+1)/(x^2-1)
critical
2
x
2
+
1
x
2
−
1
critical 2x^3+12x^2+18x
critical
2
x
3
+
1
2
x
2
+
1
8
x
critical f(x)=9x^2ln(x)
critical
f
(
x
)
=
9
x
2
ln
(
x
)
critical x^3+y^3+3xy+5
critical
x
3
+
y
3
+
3
xy
+
5
critical f(x)=(x+2y)^3+3x-24y-2(x-3y)^3
critical
f
(
x
)
=
(
x
+
2
y
)
3
+
3
x
−
2
4
y
−
2
(
x
−
3
y
)
3
critical (3x+6)/(2sqrt(x+3))
critical
3
x
+
6
2
√
x
+
3
critical f(x)=(e^x+e^{-x})/(10)
critical
f
(
x
)
=
e
x
+
e
−
x
1
0
critical f(x)=xsqrt(x-a)
critical
f
(
x
)
=
x
√
x
−
a
critical f(x)=\sqrt[3]{49-x^2}
critical
f
(
x
)
=
3
√
4
9
−
x
2
critical f(x)=-x^2+10x
critical
f
(
x
)
=
−
x
2
+
1
0
x
critical f(θ)=cos(θ)+sqrt(3)sin(θ)
critical
f
(
θ
)
=
cos
(
θ
)
+
√
3
sin
(
θ
)
critical f(x,y)=x^4+y^4+9xy
critical
f
(
x
,
y
)
=
x
4
+
y
4
+
9
xy
critical f(x)=(x^2+4)/(2x)
critical
f
(
x
)
=
x
2
+
4
2
x
critical f(x)=4x^3+11/2 x^2-15x
critical
f
(
x
)
=
4
x
3
+
1
1
2
x
2
−
1
5
x
d/(dI)(e^xInx)
d
dI
(
e
x
Inx
)
critical f(x)=(x-2)^2(x+6)
critical
f
(
x
)
=
(
x
−
2
)
2
(
x
+
6
)
critical f(x)=sin(x)+sin^3(x)
critical
f
(
x
)
=
sin
(
x
)
+
sin
3
(
x
)
critical f(x)=x^3-3x+8
critical
f
(
x
)
=
x
3
−
3
x
+
8
critical (3x)/(x-7)
critical
3
x
x
−
7
critical 4x(x^2+6x+9)
critical
4
x
(
x
2
+
6
x
+
9
)
critical f(x)=x^2-xy+y^2+3
critical
f
(
x
)
=
x
2
−
xy
+
y
2
+
3
critical f(x)=cos(x),0<= x<= 2pi
critical
f
(
x
)
=
cos
(
x
)
,
0
≤
x
≤
2
π
critical f(x)=x^3-2x^2-15x+2
critical
f
(
x
)
=
x
3
−
2
x
2
−
1
5
x
+
2
critical f(x)=|ln(x+4)|-1
critical
f
(
x
)
=
|
ln
(
x
+
4
)
|
−
1
critical f(x)=x^3-2x^2-15x
critical
f
(
x
)
=
x
3
−
2
x
2
−
1
5
x
critical f(t)=2cos(t)+sin(2t)
critical
f
(
t
)
=
2
cos
(
t
)
+
sin
(
2
t
)
critical f(x)=3x+1/x
critical
f
(
x
)
=
3
x
+
1
x
critical f(x)=3x^4+8x^3-6x^2-24x
critical
f
(
x
)
=
3
x
4
+
8
x
3
−
6
x
2
−
2
4
x
critical f(x)=4x^{1/2}-2x
critical
f
(
x
)
=
4
x
1
2
−
2
x
critical f(x)=x+ln(x)
critical
f
(
x
)
=
x
+
ln
(
x
)
critical f(x)=2.2+4.2x-1.6x^2
critical
f
(
x
)
=
2
.
2
+
4
.
2
x
−
1
.
6
x
2
critical f(x)=3x^2-2x-6
critical
f
(
x
)
=
3
x
2
−
2
x
−
6
critical-6x^2-5y^2-3xy+500x+900y-16000
critical
−
6
x
2
−
5
y
2
−
3
xy
+
5
0
0
x
+
9
0
0
y
−
1
6
0
0
0
critical f(x)=-x^3+12x^2
critical
f
(
x
)
=
−
x
3
+
1
2
x
2
critical f(x)=x^2+2xy+2y^2
critical
f
(
x
)
=
x
2
+
2
xy
+
2
y
2
critical f(x,y)=e^{4y-x^2-y^2}
critical
f
(
x
,
y
)
=
e
4
y
−
x
2
−
y
2
critical f(x,y)=4x^2+3xy^2+4y+24
critical
f
(
x
,
y
)
=
4
x
2
+
3
xy
2
+
4
y
+
2
4
critical f(x)=6x^4+2x^3
critical
f
(
x
)
=
6
x
4
+
2
x
3
critical (x-3)^2(x+8)
critical
(
x
−
3
)
2
(
x
+
8
)
critical e^{x^2-y^2}
critical
e
x
2
−
y
2
critical f(x)=2x^3-30^2+144x+11
critical
f
(
x
)
=
2
x
3
−
3
0
2
+
1
4
4
x
+
1
1
critical (2x+1)e^{-x^2}
critical
(
2
x
+
1
)
e
−
x
2
critical f(x,y)=2x^3+y^3-3x^2-3y
critical
f
(
x
,
y
)
=
2
x
3
+
y
3
−
3
x
2
−
3
y
critical f(x)=x^2+6xy+10y^2-4y+4
critical
f
(
x
)
=
x
2
+
6
xy
+
1
0
y
2
−
4
y
+
4
critical f(x,y)=-x^2-4y^2-ax+axy
critical
f
(
x
,
y
)
=
−
x
2
−
4
y
2
−
ax
+
axy
critical f(x)=(x^{3/4}-2x^{1/4})
critical
f
(
x
)
=
(
x
3
4
−
2
x
1
4
)
critical f(x)=x^4-4x^3+9
critical
f
(
x
)
=
x
4
−
4
x
3
+
9
critical f(x)=4x^{1/2}-x^{5/2}[0.4]
critical
f
(
x
)
=
4
x
1
2
−
x
5
2
[
0
.
4
]
critical f(x)=x^{-2}
critical
f
(
x
)
=
x
−
2
critical (4e^x)/(4e^x+3)
critical
4
e
x
4
e
x
+
3
critical f(x)=x^3-x+y^3-y
critical
f
(
x
)
=
x
3
−
x
+
y
3
−
y
critical f(x)=x^3-12x^2+36x-13
critical
f
(
x
)
=
x
3
−
1
2
x
2
+
3
6
x
−
1
3
critical f(x,y)=7x^2+10xy^2-7y^2x+1
critical
f
(
x
,
y
)
=
7
x
2
+
1
0
xy
2
−
7
y
2
x
+
1
critical f(x)=(x+3)^2-4(y-1)^2
critical
f
(
x
)
=
(
x
+
3
)
2
−
4
(
y
−
1
)
2
critical ((24(3x^2+4)))/((x^2-4)^3)
critical
(
2
4
(
3
x
2
+
4
)
)
(
x
2
−
4
)
3
critical-1000x^3-1000x^2+8000x+1000
critical
−
1
0
0
0
x
3
−
1
0
0
0
x
2
+
8
0
0
0
x
+
1
0
0
0
critical f(x)=2x^3-9x^2-24x+3
critical
f
(
x
)
=
2
x
3
−
9
x
2
−
2
4
x
+
3
critical f(x)=2x^3-9x^2-24x+1
critical
f
(
x
)
=
2
x
3
−
9
x
2
−
2
4
x
+
1
critical (x-2)^{2/3}
critical
(
x
−
2
)
2
3
critical f(x)= 1/3 x^3+2x^2+4x
critical
f
(
x
)
=
1
3
x
3
+
2
x
2
+
4
x
critical f(x,y)=8+76xy+38x^2+240y+(y^4)/4
critical
f
(
x
,
y
)
=
8
+
7
6
xy
+
3
8
x
2
+
2
4
0
y
+
y
4
4
critical f(x,y)=sqrt(x^2+y^2-1)+sqrt(4-x^2-y^2)
critical
f
(
x
,
y
)
=
√
x
2
+
y
2
−
1
+
√
4
−
x
2
−
y
2
critical f(x)=ln(4-x^2)
critical
f
(
x
)
=
ln
(
4
−
x
2
)
critical f(x,y)=ysqrt(x)-y^2-3x+11y
critical
f
(
x
,
y
)
=
y
√
x
−
y
2
−
3
x
+
1
1
y
critical y=3x^2-4x+7
critical
y
=
3
x
2
−
4
x
+
7
critical f(x,y)=x^2y-x^2-1/3 y^3
critical
f
(
x
,
y
)
=
x
2
y
−
x
2
−
1
3
y
3
critical f(x)=(4e^x)/(4e^x+4)
critical
f
(
x
)
=
4
e
x
4
e
x
+
4
critical f(x)=2+x+7/x
critical
f
(
x
)
=
2
+
x
+
7
x
critical y=2+12x-x^3
critical
y
=
2
+
1
2
x
−
x
3
critical f(x)=x-x^{1/3}
critical
f
(
x
)
=
x
−
x
1
3
critical f(x)=((3x^2-11))/((x^2-4))
critical
f
(
x
)
=
(
3
x
2
−
1
1
)
(
x
2
−
4
)
critical f(x)=-2x^3+36x^2-192x+7
critical
f
(
x
)
=
−
2
x
3
+
3
6
x
2
−
1
9
2
x
+
7
1
..
844
845
846
847
848
..
1324