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常见 Functions & Graphing 问题
critical f(x)x^3+3x-2
critical
f
(
x
)
x
3
+
3
x
−
2
critical 2cos(x)+sin^2(x)
critical
2
cos
(
x
)
+
sin
2
(
x
)
critical f(x)=2x^3-17x^2+19x+14
critical
f
(
x
)
=
2
x
3
−
1
7
x
2
+
1
9
x
+
1
4
critical f(x)=10xy-5x^2y-2xy^2
critical
f
(
x
)
=
1
0
xy
−
5
x
2
y
−
2
xy
2
critical f(x)=x^3+12x^2+36x
critical
f
(
x
)
=
x
3
+
1
2
x
2
+
3
6
x
critical f(x,y)=x^2-(y-1)^2
critical
f
(
x
,
y
)
=
x
2
−
(
y
−
1
)
2
critical f(x,y)=x^3-y^3+3xy
critical
f
(
x
,
y
)
=
x
3
−
y
3
+
3
xy
critical 11000-x^3+42x^2+800x
critical
1
1
0
0
0
−
x
3
+
4
2
x
2
+
8
0
0
x
critical x^3-2xy+y^2+4
critical
x
3
−
2
xy
+
y
2
+
4
critical f(x)=x^2+2xy+2y^2-6x+10y+6
critical
f
(
x
)
=
x
2
+
2
xy
+
2
y
2
−
6
x
+
1
0
y
+
6
critical (8x^2-24x)/(3(x+1)^{1/3)}
critical
8
x
2
−
2
4
x
3
(
x
+
1
)
1
3
critical f(x)=6x^2+2x-12
critical
f
(
x
)
=
6
x
2
+
2
x
−
1
2
critical 8-(x+3)^2
critical
8
−
(
x
+
3
)
2
critical x^2-16
critical
x
2
−
1
6
critical f(x)=xsqrt(x+7)
critical
f
(
x
)
=
x
√
x
+
7
critical (x+3)/(x-2)
critical
x
+
3
x
−
2
critical 1/4 x^4+1/3 x^3-x^2+2/3
critical
1
4
x
4
+
1
3
x
3
−
x
2
+
2
3
critical (x^2-9)/(x-5)
critical
x
2
−
9
x
−
5
critical f(x)=-x^4+4x^3+8x^2
critical
f
(
x
)
=
−
x
4
+
4
x
3
+
8
x
2
critical g(y)=((y-1))/(y^2-y+1)
critical
g
(
y
)
=
(
y
−
1
)
y
2
−
y
+
1
critical-3x^2+6x
critical
−
3
x
2
+
6
x
critical f(x,y)=x^3+x^2y+x-y
critical
f
(
x
,
y
)
=
x
3
+
x
2
y
+
x
−
y
critical f(x)=ln(x)+1
critical
f
(
x
)
=
ln
(
x
)
+
1
critical y=x^3-3x^2+b
critical
y
=
x
3
−
3
x
2
+
b
critical f(x)=(9x^2ln(x))
critical
f
(
x
)
=
(
9
x
2
ln
(
x
)
)
critical (x^3+1)/(x^2)
critical
x
3
+
1
x
2
critical f(x)=x^{2/3}(x^2-8)
critical
f
(
x
)
=
x
2
3
(
x
2
−
8
)
critical f(x)=ln(x)+ln(64-x^2)
critical
f
(
x
)
=
ln
(
x
)
+
ln
(
6
4
−
x
2
)
critical ln(1-ln(x))
critical
ln
(
1
−
ln
(
x
)
)
critical f(x)=x^{2/3}(x^2-9)
critical
f
(
x
)
=
x
2
3
(
x
2
−
9
)
critical f(x)=g(x)=2+(x-5)^3
critical
f
(
x
)
=
g
(
x
)
=
2
+
(
x
−
5
)
3
critical x^3+y^3+3x^2-18y+5
critical
x
3
+
y
3
+
3
x
2
−
1
8
y
+
5
critical 1-sin(x)
critical
1
−
sin
(
x
)
critical f(x)=-5x-8
critical
f
(
x
)
=
−
5
x
−
8
critical f(x)=x^3ln(x),(0,infinity)
critical
f
(
x
)
=
x
3
ln
(
x
)
,
(
0
,
∞
)
critical x^2y+y^3-27y
critical
x
2
y
+
y
3
−
2
7
y
critical 1/3 y^3+4xy-9y-x^2
critical
1
3
y
3
+
4
xy
−
9
y
−
x
2
critical f(x)=3x^3-5x
critical
f
(
x
)
=
3
x
3
−
5
x
critical f(x,y)=12x-x^3-4y^2
critical
f
(
x
,
y
)
=
1
2
x
−
x
3
−
4
y
2
critical f(x)=ln(1+x)
critical
f
(
x
)
=
ln
(
1
+
x
)
critical f(x,y)=1+4x+4y^3-x^4-y^4
critical
f
(
x
,
y
)
=
1
+
4
x
+
4
y
3
−
x
4
−
y
4
critical f(x)=3x^3-9x
critical
f
(
x
)
=
3
x
3
−
9
x
critical f(x)=3x+1/2 sin(6x)
critical
f
(
x
)
=
3
x
+
1
2
sin
(
6
x
)
critical f(x)= 1/3 x^3+3/2 x^2-18x
critical
f
(
x
)
=
1
3
x
3
+
3
2
x
2
−
1
8
x
critical y=2x^3+3x^2-36x
critical
y
=
2
x
3
+
3
x
2
−
3
6
x
critical (-x^2-9)/((x^2-9)^2)
critical
−
x
2
−
9
(
x
2
−
9
)
2
critical x^5+5x^4-40x^2
critical
x
5
+
5
x
4
−
4
0
x
2
critical f(x)=4x^4-4x^3
critical
f
(
x
)
=
4
x
4
−
4
x
3
critical-2^x
critical
−
2
x
critical f(x)= 1/3 x^3-3/2 x^2-10x
critical
f
(
x
)
=
1
3
x
3
−
3
2
x
2
−
1
0
x
critical 90x^2e^{-1.2x}
critical
9
0
x
2
e
−
1
.
2
x
critical x^4+4x
critical
x
4
+
4
x
critical-496e^{-1.5x^2}+498
critical
−
4
9
6
e
−
1
.
5
x
2
+
4
9
8
critical f(x)=3x^2-12x+5
critical
f
(
x
)
=
3
x
2
−
1
2
x
+
5
critical x^3-2x^2-x+1
critical
x
3
−
2
x
2
−
x
+
1
critical f(x)=5x^4-6x^2+1
critical
f
(
x
)
=
5
x
4
−
6
x
2
+
1
critical 2x^4+4x^2-30
critical
2
x
4
+
4
x
2
−
3
0
critical f(x,y)=x^3-3xy^2+9y^2
critical
f
(
x
,
y
)
=
x
3
−
3
xy
2
+
9
y
2
critical 7x^2ln(x)
critical
7
x
2
ln
(
x
)
critical f(x,y)=3x^3-5y^2-255x+70y+23
critical
f
(
x
,
y
)
=
3
x
3
−
5
y
2
−
2
5
5
x
+
7
0
y
+
2
3
critical f(x)=10+12x-3x^2-x^3
critical
f
(
x
)
=
1
0
+
1
2
x
−
3
x
2
−
x
3
critical f(x)=(-8)/(x^{4/3)(6-x)^{5/3}}
critical
f
(
x
)
=
−
8
x
4
3
(
6
−
x
)
5
3
critical x^{2/3}(5/2-x)
critical
x
2
3
(
5
2
−
x
)
critical z=xy-2x-1-4y-1+8
critical
z
=
xy
−
2
x
−
1
−
4
y
−
1
+
8
critical C(x)=2x+(300000)/x ,1<= x<= 300
critical
C
(
x
)
=
2
x
+
3
0
0
0
0
0
x
,
1
≤
x
≤
3
0
0
critical (x+2)/(x-1)
critical
x
+
2
x
−
1
critical f(x)=1-3x+5x^2-x^3
critical
f
(
x
)
=
1
−
3
x
+
5
x
2
−
x
3
critical (x-1)(x-2)(x-3)
critical
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
critical y=-(15)/(x^2+5)
critical
y
=
−
1
5
x
2
+
5
critical f(x)=x^4+y^4-6x^2y^2-2x^2+2y^2
critical
f
(
x
)
=
x
4
+
y
4
−
6
x
2
y
2
−
2
x
2
+
2
y
2
critical f(x)=x^4+y^4+x^2y^2
critical
f
(
x
)
=
x
4
+
y
4
+
x
2
y
2
critical Q(x)=xe^x
critical
Q
(
x
)
=
xe
x
critical (x-2)^3(3x+14)
critical
(
x
−
2
)
3
(
3
x
+
1
4
)
critical y= x/(x^2+49)
critical
y
=
x
x
2
+
4
9
critical f(x)=12x^2+2x^3
critical
f
(
x
)
=
1
2
x
2
+
2
x
3
critical f(x)=2+(x-5)3
critical
f
(
x
)
=
2
+
(
x
−
5
)
3
critical 6x^2-2x^3+3y^2+6xy
critical
6
x
2
−
2
x
3
+
3
y
2
+
6
xy
critical f(x)=(x^3)/3-x^2-15x-1
critical
f
(
x
)
=
x
3
3
−
x
2
−
1
5
x
−
1
critical xy+3/x+9/y
critical
xy
+
3
x
+
9
y
critical f(x)=ln(x^2+1)(x^2-1)
critical
f
(
x
)
=
ln
(
x
2
+
1
)
(
x
2
−
1
)
critical f(x)= 1/2 x+sin(x)
critical
f
(
x
)
=
1
2
x
+
sin
(
x
)
critical x^2y-2xy+3y^3-3y
critical
x
2
y
−
2
xy
+
3
y
3
−
3
y
critical f(x)=3x+(108)/x
critical
f
(
x
)
=
3
x
+
1
0
8
x
critical 2x^3-39x^2+180x+6
critical
2
x
3
−
3
9
x
2
+
1
8
0
x
+
6
critical f(x)=9-x^2
critical
f
(
x
)
=
9
−
x
2
critical f(x)=x^3-In(x(x^2+1))
critical
f
(
x
)
=
x
3
−
In
(
x
(
x
2
+
1
)
)
critical f(x)=(x^2-9)^2
critical
f
(
x
)
=
(
x
2
−
9
)
2
critical x^2-x^2y^2+y^2
critical
x
2
−
x
2
y
2
+
y
2
critical f(x)=2x^2+3x-1
critical
f
(
x
)
=
2
x
2
+
3
x
−
1
critical x^{1/3}(x+4)
critical
x
1
3
(
x
+
4
)
critical (x^2+12)(1-x^2)
critical
(
x
2
+
1
2
)
(
1
−
x
2
)
critical f(x)=-16x^3+20x^2+19x+3
critical
f
(
x
)
=
−
1
6
x
3
+
2
0
x
2
+
1
9
x
+
3
critical 6x^8(3-x)^7
critical
6
x
8
(
3
−
x
)
7
critical f(x,y)=e^{xy^2+1}
critical
f
(
x
,
y
)
=
e
xy
2
+
1
critical f(x)=x^{1/3}(x^2-64)
critical
f
(
x
)
=
x
1
3
(
x
2
−
6
4
)
critical f(x,y)=x^2y-4y^3
critical
f
(
x
,
y
)
=
x
2
y
−
4
y
3
critical 2sqrt(x)e^{-x}
critical
2
√
x
e
−
x
critical y=x^3-6x^2+9x
critical
y
=
x
3
−
6
x
2
+
9
x
critical f(x)=x^2-18ln(3x)
critical
f
(
x
)
=
x
2
−
1
8
ln
(
3
x
)
critical f(x)=1-sqrt(x)
critical
f
(
x
)
=
1
−
√
x
1
..
843
844
845
846
847
..
1324