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常见 Functions & Graphing 问题
extreme x^2+14x+46.2
extreme
x
2
+
1
4
x
+
4
6
.
2
extreme f(x)=x+ln(x^2-1)
extreme
f
(
x
)
=
x
+
ln
(
x
2
−
1
)
extreme f(x)=2x^3-33x^2+168x+7
extreme
f
(
x
)
=
2
x
3
−
3
3
x
2
+
1
6
8
x
+
7
extreme P(x,y)=10x^2-10y^2
extreme
P
(
x
,
y
)
=
1
0
x
2
−
1
0
y
2
extreme f(x)=x^2e^{1-x}
extreme
f
(
x
)
=
x
2
e
1
−
x
extreme (3-x)(x-5)^2
extreme
(
3
−
x
)
(
x
−
5
)
2
extreme f(x,y)= 1/x+1/y-xy+3
extreme
f
(
x
,
y
)
=
1
x
+
1
y
−
xy
+
3
extreme f(x)=x^3+y^3+9x^2-9y^2-2
extreme
f
(
x
)
=
x
3
+
y
3
+
9
x
2
−
9
y
2
−
2
extreme f(x)=((x))/((6x+2)),5<= x<= 8
extreme
f
(
x
)
=
(
x
)
(
6
x
+
2
)
,
5
≤
x
≤
8
extreme f(x,y)=(x-1)^3+(x-1)^2+(y+1)^2
extreme
f
(
x
,
y
)
=
(
x
−
1
)
3
+
(
x
−
1
)
2
+
(
y
+
1
)
2
extreme f(x,y)=x^2-2y^2-x+y
extreme
f
(
x
,
y
)
=
x
2
−
2
y
2
−
x
+
y
extreme f(x)=x^4-18x^2+1,-6<= x<= 6
extreme
f
(
x
)
=
x
4
−
1
8
x
2
+
1
,
−
6
≤
x
≤
6
extreme f(x)=3x^5-25x^3+60x
extreme
f
(
x
)
=
3
x
5
−
2
5
x
3
+
6
0
x
extreme x^2+xy+y^2-7x-3y
extreme
x
2
+
xy
+
y
2
−
7
x
−
3
y
extreme 10x^{1/2}-x[100]
extreme
1
0
x
1
2
−
x
[
1
0
0
]
extreme f(x)=2x^3-2x^2-2x+6
extreme
f
(
x
)
=
2
x
3
−
2
x
2
−
2
x
+
6
extreme f(x)=(4x^2-64)^{1/5}
extreme
f
(
x
)
=
(
4
x
2
−
6
4
)
1
5
extreme f(x,y)=e^{y^2+x^3-6xy-6x+2y}
extreme
f
(
x
,
y
)
=
e
y
2
+
x
3
−
6
xy
−
6
x
+
2
y
extreme (2x+4)/(x^2-16)
extreme
2
x
+
4
x
2
−
1
6
extreme f(x)=x^2 1/(x-1)
extreme
f
(
x
)
=
x
2
1
x
−
1
extreme f(x)=x[18-2(x)]^2
extreme
f
(
x
)
=
x
[
1
8
−
2
(
x
)
]
2
extreme f(x,y)=x^2-3y^2-8x+9y+3xy
extreme
f
(
x
,
y
)
=
x
2
−
3
y
2
−
8
x
+
9
y
+
3
xy
extreme f(d,y)= d/(d^2)(y)
extreme
f
(
d
,
y
)
=
d
d
2
(
y
)
extreme y=-5cos(3x)-2
extreme
y
=
−
5
cos
(
3
x
)
−
2
extreme f(x,y)=3x^{1/3}y^{1/3}
extreme
f
(
x
,
y
)
=
3
x
1
3
y
1
3
extreme f(x)=(x^2)/(sqrt(x)-1)
extreme
f
(
x
)
=
x
2
√
x
−
1
extreme P(-8.5)Q(-4.11)
extreme
P
(
−
8
.
5
)
Q
(
−
4
.
1
1
)
extreme x^3+8x^2-6x-4
extreme
x
3
+
8
x
2
−
6
x
−
4
extreme f(x)=-13/9 x^2+8/3 x^2+37/10
extreme
f
(
x
)
=
−
1
3
9
x
2
+
8
3
x
2
+
3
7
1
0
extreme ((x-4))/(x^2)
extreme
(
x
−
4
)
x
2
extreme f(x)=(2x-6)/(sqrt(x^2+7)-4)
extreme
f
(
x
)
=
2
x
−
6
√
x
2
+
7
−
4
extreme f(x)=(5+x)+(1000+100x)
extreme
f
(
x
)
=
(
5
+
x
)
+
(
1
0
0
0
+
1
0
0
x
)
extreme f(x)=-(x/3)^3+2x^2+12x+1
extreme
f
(
x
)
=
−
(
x
3
)
3
+
2
x
2
+
1
2
x
+
1
extreme y=5+6x-8x^3
extreme
y
=
5
+
6
x
−
8
x
3
extreme f(x)=(2x+4)/(x^2+4)
extreme
f
(
x
)
=
2
x
+
4
x
2
+
4
extreme f(x)=(6x+1)e^{8x-x^2}
extreme
f
(
x
)
=
(
6
x
+
1
)
e
8
x
−
x
2
extreme f(x)=x^4-3x^2,-2<= x<= 0
extreme
f
(
x
)
=
x
4
−
3
x
2
,
−
2
≤
x
≤
0
extreme f(x)=4xe^{-x^2}
extreme
f
(
x
)
=
4
xe
−
x
2
extreme y=15xe^{-0.05x}-30
extreme
y
=
1
5
xe
−
0
.
0
5
x
−
3
0
extreme f(x)=(-4x)/(x^2+6),(0,6)
extreme
f
(
x
)
=
−
4
x
x
2
+
6
,
(
0
,
6
)
extreme f(x)=2x^3+15x^2-36x+7,-6<x<2
extreme
f
(
x
)
=
2
x
3
+
1
5
x
2
−
3
6
x
+
7
,
−
6
<
x
<
2
extreme f(x)=13e^{-x},(0,4)
extreme
f
(
x
)
=
1
3
e
−
x
,
(
0
,
4
)
extreme-y^2+120y
extreme
−
y
2
+
1
2
0
y
extreme f(x)=x-1/x+2/(x^3),[0,infinity ]
extreme
f
(
x
)
=
x
−
1
x
+
2
x
3
,
[
0
,
∞
]
extreme y=2x_{1}+4x_{2}
extreme
y
=
2
x
1
+
4
x
2
extreme f(x,y)=-sqrt(25-x^2-y^2)
extreme
f
(
x
,
y
)
=
−
√
2
5
−
x
2
−
y
2
extreme f(x)=(x+5)/(x-3),(-5,2)
extreme
f
(
x
)
=
x
+
5
x
−
3
,
(
−
5
,
2
)
extreme f(x)=-1/3 x^3-x^2-12
extreme
f
(
x
)
=
−
1
3
x
3
−
x
2
−
1
2
extreme f(x)=-(24x)/(x^2+9)
extreme
f
(
x
)
=
−
2
4
x
x
2
+
9
extreme-2x^2-12x-17
extreme
−
2
x
2
−
1
2
x
−
1
7
extreme f(x)=5xe^{-x},0<= x<= 2
extreme
f
(
x
)
=
5
xe
−
x
,
0
≤
x
≤
2
extreme f(x)=2x^3-9x^2+60x+8
extreme
f
(
x
)
=
2
x
3
−
9
x
2
+
6
0
x
+
8
extreme f(x)=150x-2x^3
extreme
f
(
x
)
=
1
5
0
x
−
2
x
3
extreme f(x)=(x^2-2x-8)^{1/3}
extreme
f
(
x
)
=
(
x
2
−
2
x
−
8
)
1
3
extreme f(x)=x^2-10x-7
extreme
f
(
x
)
=
x
2
−
1
0
x
−
7
extreme f(x)=(4x)^x,0.05<= x<= 1
extreme
f
(
x
)
=
(
4
x
)
x
,
0
.
0
5
≤
x
≤
1
extreme f(x)=ln(x^2+5x+9)
extreme
f
(
x
)
=
ln
(
x
2
+
5
x
+
9
)
extreme f(x)=x^{1/2}-x^{3/2}
extreme
f
(
x
)
=
x
1
2
−
x
3
2
extreme f(χ)=χ^2e^{-4χ^2}
extreme
f
(
χ
)
=
χ
2
e
−
4
χ
2
extreme f(x)=(y-800)/(-2)
extreme
f
(
x
)
=
y
−
8
0
0
−
2
extreme (x-1)e^{1/x}
extreme
(
x
−
1
)
e
1
x
extreme f(x)=x^4+x^2(y-2)+3(y-1)^2
extreme
f
(
x
)
=
x
4
+
x
2
(
y
−
2
)
+
3
(
y
−
1
)
2
extreme f(x,y)=2e^xln(1+y)
extreme
f
(
x
,
y
)
=
2
e
x
ln
(
1
+
y
)
extreme f(x)=9(x-4)^2+5
extreme
f
(
x
)
=
9
(
x
−
4
)
2
+
5
extreme f(x,y)=2x^2+y^2+xy^2
extreme
f
(
x
,
y
)
=
2
x
2
+
y
2
+
xy
2
extreme f(x)=-16+4ln(x)
extreme
f
(
x
)
=
−
1
6
+
4
ln
(
x
)
extreme f(x,y)=x^2-2y^2+xy-3x+3y+4
extreme
f
(
x
,
y
)
=
x
2
−
2
y
2
+
xy
−
3
x
+
3
y
+
4
extreme f(x)=(x^3)/3+x^2-8x
extreme
f
(
x
)
=
x
3
3
+
x
2
−
8
x
extreme-x^4y^2-x^4+2x^3y+2x^2y+x^2-2x-2
extreme
−
x
4
y
2
−
x
4
+
2
x
3
y
+
2
x
2
y
+
x
2
−
2
x
−
2
extreme f(x*y)=xy+8^{xy}
extreme
f
(
x
·
y
)
=
xy
+
8
xy
extreme f(x)=x^2-6x+12
extreme
f
(
x
)
=
x
2
−
6
x
+
1
2
extreme f(t)= x/(x+25)[0.9]
extreme
f
(
t
)
=
x
x
+
2
5
[
0
.
9
]
extreme f(x)=-x^3+3x^2+429x+5242
extreme
f
(
x
)
=
−
x
3
+
3
x
2
+
4
2
9
x
+
5
2
4
2
extreme f(t)=108t-t^3
extreme
f
(
t
)
=
1
0
8
t
−
t
3
extreme f(x)=2x^3+6x^2-90x+1,-5<= x<= 7
extreme
f
(
x
)
=
2
x
3
+
6
x
2
−
9
0
x
+
1
,
−
5
≤
x
≤
7
extreme f(x)=x^4+2x^3-2x^2+2x+1
extreme
f
(
x
)
=
x
4
+
2
x
3
−
2
x
2
+
2
x
+
1
extreme 1/(sqrt(2pi))e^{-(x-3)^{2/2}}
extreme
1
√
2
π
e
−
(
x
−
3
)
2
2
extreme f(x)=4(e^{-0.05x}-e^{-0.55x})
extreme
f
(
x
)
=
4
(
e
−
0
.
0
5
x
−
e
−
0
.
5
5
x
)
extreme f(x)=-x^3+1.5x^2+36x+2
extreme
f
(
x
)
=
−
x
3
+
1
.
5
x
2
+
3
6
x
+
2
extreme f(x,y)=2x^2+y^2-4x+6y
extreme
f
(
x
,
y
)
=
2
x
2
+
y
2
−
4
x
+
6
y
extreme y=xe^{-2x}
extreme
y
=
xe
−
2
x
extreme f(x)=x+3y^2=25
extreme
f
(
x
)
=
x
+
3
y
2
=
2
5
extreme f(x)=110.2x-0.4x^2-20.2-2000
extreme
f
(
x
)
=
1
1
0
.
2
x
−
0
.
4
x
2
−
2
0
.
2
−
2
0
0
0
extreme f(x)=(x^3)/3-16x^2+240x-36
extreme
f
(
x
)
=
x
3
3
−
1
6
x
2
+
2
4
0
x
−
3
6
extreme y=4x^3-8x
extreme
y
=
4
x
3
−
8
x
extreme f(x)= 7/(4-3sin^2(x))
extreme
f
(
x
)
=
7
4
−
3
sin
2
(
x
)
extreme |x^2-5|,1<x<7
extreme
|
x
2
−
5
|
,
1
<
x
<
7
extreme (x-7)(x-5)^2(x-3)(x-1)
extreme
(
x
−
7
)
(
x
−
5
)
2
(
x
−
3
)
(
x
−
1
)
extreme (400)/(1+8e^{0.05x)}
extreme
4
0
0
1
+
8
e
0
.
0
5
x
extreme 1+(ln(x))
extreme
1
+
(
ln
(
x
)
)
extreme f(x,y)=3x^2+3x-2y+4y^2-12xy
extreme
f
(
x
,
y
)
=
3
x
2
+
3
x
−
2
y
+
4
y
2
−
1
2
xy
extreme f(x,y)=x^2-y^2-9x-2y
extreme
f
(
x
,
y
)
=
x
2
−
y
2
−
9
x
−
2
y
extreme f(x)=2x^3-9x^2+3,-2<= x<= 2
extreme
f
(
x
)
=
2
x
3
−
9
x
2
+
3
,
−
2
≤
x
≤
2
extreme f(x,y)=x^3+y^3+3xy^2-18x-18y
extreme
f
(
x
,
y
)
=
x
3
+
y
3
+
3
xy
2
−
1
8
x
−
1
8
y
extreme f(x)=2x^4-36x^2
extreme
f
(
x
)
=
2
x
4
−
3
6
x
2
extreme f(x)=25(x^2-y^2)-2(x^2+y^2)^2
extreme
f
(
x
)
=
2
5
(
x
2
−
y
2
)
−
2
(
x
2
+
y
2
)
2
extreme f(x)=2x^3+4x^2+2x
extreme
f
(
x
)
=
2
x
3
+
4
x
2
+
2
x
extreme f(x,y)=80x^{4/10}y^{2/10}
extreme
f
(
x
,
y
)
=
8
0
x
4
1
0
y
2
1
0
extreme 5(x-4)^{2/3}
extreme
5
(
x
−
4
)
2
3
extreme f(x)=5x^2y+3xy^8+23
extreme
f
(
x
)
=
5
x
2
y
+
3
xy
8
+
2
3
1
..
827
828
829
830
831
..
839
