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常见 Functions & Graphing 问题
critical e^{3x}-3e^x
critical
e
3
x
−
3
e
x
critical f(x)=(x^2-5x+6)/(x^2)
critical
f
(
x
)
=
x
2
−
5
x
+
6
x
2
critical y=3x^4+4x^3-12x^2
critical
y
=
3
x
4
+
4
x
3
−
1
2
x
2
critical f(x)=((x^3+1)/(x^2-1))
critical
f
(
x
)
=
(
x
3
+
1
x
2
−
1
)
critical f(x)=4x^3+3x^2-6x
critical
f
(
x
)
=
4
x
3
+
3
x
2
−
6
x
critical f(x)=6x^5-90x^3
critical
f
(
x
)
=
6
x
5
−
9
0
x
3
critical f(x)=5x^{2/3}+x^{5/3}
critical
f
(
x
)
=
5
x
2
3
+
x
5
3
critical x^2e^{-2x}
critical
x
2
e
−
2
x
critical (x+2)/(x-4)+2
critical
x
+
2
x
−
4
+
2
critical y=3x^4+4x^3-12x^2+7
critical
y
=
3
x
4
+
4
x
3
−
1
2
x
2
+
7
critical 3x^2ln(x)
critical
3
x
2
ln
(
x
)
critical e^{x^2+y^2}
critical
e
x
2
+
y
2
critical f(x)=-x^2-4x-4
critical
f
(
x
)
=
−
x
2
−
4
x
−
4
critical f(x)=x^2-20x
critical
f
(
x
)
=
x
2
−
2
0
x
critical f(x,y)=3y^3+5x^2y-24x^2-24y^2-2
critical
f
(
x
,
y
)
=
3
y
3
+
5
x
2
y
−
2
4
x
2
−
2
4
y
2
−
2
critical x^4-18x^2
critical
x
4
−
1
8
x
2
critical x^{4/5}(x-8)^2
critical
x
4
5
(
x
−
8
)
2
critical f(x)=(x^{16})/(x^{17)+4}
critical
f
(
x
)
=
x
1
6
x
1
7
+
4
critical f(x)=(7x)/(x^2-4)
critical
f
(
x
)
=
7
x
x
2
−
4
critical f(x)=2cos(x)-sin(2x)
critical
f
(
x
)
=
2
cos
(
x
)
−
sin
(
2
x
)
critical f(x,y)=xy^2+x^2+y
critical
f
(
x
,
y
)
=
xy
2
+
x
2
+
y
critical f(x,y)=x^2y+y^3-12y
critical
f
(
x
,
y
)
=
x
2
y
+
y
3
−
1
2
y
critical f(x)= x/(1-x)-(x^2)/(1+x)
critical
f
(
x
)
=
x
1
−
x
−
x
2
1
+
x
critical 1/(sqrt(x))
critical
1
√
x
critical {x^2:x<-2,ln(x+5):x>=-2}
critical
{
x
2
:
x
<
−
2
,
ln
(
x
+
5
)
:
x
≥
−
2
}
critical f(x)=x^4+4/3 x^3-4x^2
critical
f
(
x
)
=
x
4
+
4
3
x
3
−
4
x
2
critical x^2+1/(x^2)
critical
x
2
+
1
x
2
critical x^4-7x^3
critical
x
4
−
7
x
3
critical f(x)=x^4+y^4
critical
f
(
x
)
=
x
4
+
y
4
critical f(x)=x^3+6x^2-8y+25=13
critical
f
(
x
)
=
x
3
+
6
x
2
−
8
y
+
2
5
=
1
3
critical f(x)=e^{4x}(80x^2+5)
critical
f
(
x
)
=
e
4
x
(
8
0
x
2
+
5
)
critical xy+5x-5
critical
xy
+
5
x
−
5
critical f(x,y)=4x-9y+2xy-x^2+y^3
critical
f
(
x
,
y
)
=
4
x
−
9
y
+
2
xy
−
x
2
+
y
3
critical y=x^2-3x+8
critical
y
=
x
2
−
3
x
+
8
critical f(x)=2x^3-3x^2-12x+6
critical
f
(
x
)
=
2
x
3
−
3
x
2
−
1
2
x
+
6
critical f(x)=-cos^2(x)
critical
f
(
x
)
=
−
cos
2
(
x
)
critical y=2x^3-24x+5
critical
y
=
2
x
3
−
2
4
x
+
5
critical (x-1)^2(x-3)^2
critical
(
x
−
1
)
2
(
x
−
3
)
2
critical (6x^2)/(x^2-16)
critical
6
x
2
x
2
−
1
6
critical y=x^3+x^2-x
critical
y
=
x
3
+
x
2
−
x
critical f(x,y)=-x^4+x^2+y^2+3
critical
f
(
x
,
y
)
=
−
x
4
+
x
2
+
y
2
+
3
critical f(x)=x^2-6x+4
critical
f
(
x
)
=
x
2
−
6
x
+
4
critical f(x)= 1/(x^2-3x+2)
critical
f
(
x
)
=
1
x
2
−
3
x
+
2
critical \sqrt[3]{xy}
critical
3
√
xy
critical f(x)=yxe^{-(x^2+y^2)}
critical
f
(
x
)
=
yxe
−
(
x
2
+
y
2
)
critical f(x)=x^3-6x^2+9x+15
critical
f
(
x
)
=
x
3
−
6
x
2
+
9
x
+
1
5
critical f(x)=x+2ln(x^2+1)
critical
f
(
x
)
=
x
+
2
ln
(
x
2
+
1
)
critical f(x)=(x^3)/3+(x^2)/2-2x
critical
f
(
x
)
=
x
3
3
+
x
2
2
−
2
x
critical |sin(x)|
critical
|
sin
(
x
)
|
critical f(x)=x^4-8x+10
critical
f
(
x
)
=
x
4
−
8
x
+
1
0
critical f(x)= 6/(x+2)
critical
f
(
x
)
=
6
x
+
2
critical f(x)=3x^2-4x+5
critical
f
(
x
)
=
3
x
2
−
4
x
+
5
critical f(x)=2x^3+6x^2-18x+1
critical
f
(
x
)
=
2
x
3
+
6
x
2
−
1
8
x
+
1
critical f(x,y)=x^3+xy+y^2
critical
f
(
x
,
y
)
=
x
3
+
xy
+
y
2
critical f(x)=4x+sin(4x)
critical
f
(
x
)
=
4
x
+
sin
(
4
x
)
critical f(x,y)=-4xy+x^4+y^4
critical
f
(
x
,
y
)
=
−
4
xy
+
x
4
+
y
4
critical f(x)=x^{4/5}(9x-36)^2
critical
f
(
x
)
=
x
4
5
(
9
x
−
3
6
)
2
critical f(x)=x^2-3x+2
critical
f
(
x
)
=
x
2
−
3
x
+
2
critical xsqrt(x^2+36)
critical
x
√
x
2
+
3
6
critical (2x)/(x^2-16)
critical
2
x
x
2
−
1
6
critical f(x)=-(x^2+8x+12)
critical
f
(
x
)
=
−
(
x
2
+
8
x
+
1
2
)
critical 2sqrt(x)-4x
critical
2
√
x
−
4
x
critical f(x)=x^{1/3}+bx^{4/3}
critical
f
(
x
)
=
x
1
3
+
bx
4
3
critical f(x)=(x-1)^2+3
critical
f
(
x
)
=
(
x
−
1
)
2
+
3
critical f(x)=sqrt(x^2-16)
critical
f
(
x
)
=
√
x
2
−
1
6
critical f(x,y)=x^2y-2xy-3xy^2
critical
f
(
x
,
y
)
=
x
2
y
−
2
xy
−
3
xy
2
critical f(x)= x/(x^2+7x+10)
critical
f
(
x
)
=
x
x
2
+
7
x
+
1
0
critical f(x)=(x^2)/(1-x^3)
critical
f
(
x
)
=
x
2
1
−
x
3
critical y=4x^3-x^4
critical
y
=
4
x
3
−
x
4
critical x^2-3xy-y^2
critical
x
2
−
3
xy
−
y
2
critical f(x)=9x+1/x
critical
f
(
x
)
=
9
x
+
1
x
critical f(x)=sqrt(x^2-25)
critical
f
(
x
)
=
√
x
2
−
2
5
extreme f(x,y)=x^2e^y
extreme
f
(
x
,
y
)
=
x
2
e
y
critical f(x)=3x^4-4x^3-12x^2+6
critical
f
(
x
)
=
3
x
4
−
4
x
3
−
1
2
x
2
+
6
critical f(x)= 1/2 x^2-2x^2+3x+5
critical
f
(
x
)
=
1
2
x
2
−
2
x
2
+
3
x
+
5
critical f(x)= 4/(x^2-16)
critical
f
(
x
)
=
4
x
2
−
1
6
critical x^4-2x^2-8
critical
x
4
−
2
x
2
−
8
critical f(x)=x(16-x)^3
critical
f
(
x
)
=
x
(
1
6
−
x
)
3
critical f(x,y)=x^2-3xy+6y^2+5x-2y+8
critical
f
(
x
,
y
)
=
x
2
−
3
xy
+
6
y
2
+
5
x
−
2
y
+
8
critical x^2-8ln(x)
critical
x
2
−
8
ln
(
x
)
critical y=2x^3-3x^2-36x
critical
y
=
2
x
3
−
3
x
2
−
3
6
x
critical f(x)=8x^3-24x+12
critical
f
(
x
)
=
8
x
3
−
2
4
x
+
1
2
critical 12x^3-12x
critical
1
2
x
3
−
1
2
x
critical f(x)=(1-ln(x))/(x^2)
critical
f
(
x
)
=
1
−
ln
(
x
)
x
2
critical f(x)=sin(x)+cos(x),(0,2pi)
critical
f
(
x
)
=
sin
(
x
)
+
cos
(
x
)
,
(
0
,
2
π
)
critical f(x)=sin(x/2)
critical
f
(
x
)
=
sin
(
x
2
)
critical f(x,y)=3x^3y+y^2
critical
f
(
x
,
y
)
=
3
x
3
y
+
y
2
critical f(x,y)=3x^2-2xy+y^2-8y
critical
f
(
x
,
y
)
=
3
x
2
−
2
xy
+
y
2
−
8
y
critical f(x,y)=x^2-2xy+2y^2-2y
critical
f
(
x
,
y
)
=
x
2
−
2
xy
+
2
y
2
−
2
y
critical f(x)=-4x^4
critical
f
(
x
)
=
−
4
x
4
critical f(x)=5x^3+8x
critical
f
(
x
)
=
5
x
3
+
8
x
critical f(x)=-x^3+6x^2+63x
critical
f
(
x
)
=
−
x
3
+
6
x
2
+
6
3
x
critical h(t)=t^{3/4}-6t^{1/4}
critical
h
(
t
)
=
t
3
4
−
6
t
1
4
critical f(x)=(x-3)(x-11)^3
critical
f
(
x
)
=
(
x
−
3
)
(
x
−
1
1
)
3
critical f(x)=x^3-3x^2-9x+11
critical
f
(
x
)
=
x
3
−
3
x
2
−
9
x
+
1
1
critical f(x,y)=x^3+2x^2y-7xy^2+4y^3
critical
f
(
x
,
y
)
=
x
3
+
2
x
2
y
−
7
xy
2
+
4
y
3
critical f(x)=2x^3-3xy+3y^3
critical
f
(
x
)
=
2
x
3
−
3
xy
+
3
y
3
critical f(x)=x^5e^{6x}
critical
f
(
x
)
=
x
5
e
6
x
critical f(x)=x(24-2x)^2
critical
f
(
x
)
=
x
(
2
4
−
2
x
)
2
critical f(x)=x^4+y^4-2(x-y)^2
critical
f
(
x
)
=
x
4
+
y
4
−
2
(
x
−
y
)
2
1
..
835
836
837
838
839
..
1324