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常见 Functions & Graphing 问题
extreme 2x^2-6x+(20)/x+30
extreme
2
x
2
−
6
x
+
2
0
x
+
3
0
extreme f(x)=x^2-8x,-infinity <x<= 8
extreme
f
(
x
)
=
x
2
−
8
x
,
−
∞
<
x
≤
8
extreme 5x+5sin(x),0<= x<= 2pi
extreme
5
x
+
5
sin
(
x
)
,
0
≤
x
≤
2
π
extreme f(x)=106x-x^2-950
extreme
f
(
x
)
=
1
0
6
x
−
x
2
−
9
5
0
extreme f(x)=(-3x)/(sqrt(x^2+6))
extreme
f
(
x
)
=
−
3
x
√
x
2
+
6
extreme f(x)= 1/(x^2-4x-21)
extreme
f
(
x
)
=
1
x
2
−
4
x
−
2
1
extreme P(x,y)=16x^2-9y^2
extreme
P
(
x
,
y
)
=
1
6
x
2
−
9
y
2
extreme f(x)=1920x-10x^3
extreme
f
(
x
)
=
1
9
2
0
x
−
1
0
x
3
extreme f(x)=100e^{-0.062*x}
extreme
f
(
x
)
=
1
0
0
e
−
0
.
0
6
2
·
x
extreme f(x)=7sin^2(x)-14cos(x)
extreme
f
(
x
)
=
7
sin
2
(
x
)
−
1
4
cos
(
x
)
extreme f(x)=-3x^2-30x-21
extreme
f
(
x
)
=
−
3
x
2
−
3
0
x
−
2
1
extreme y=z-x
extreme
y
=
z
−
x
extreme S(r,α)=rα
extreme
S
(
r
,
α
)
=
r
α
extreme f(x,y)=5004+x^2+y^2
extreme
f
(
x
,
y
)
=
5
0
0
4
+
x
2
+
y
2
extreme f(x)=2x^3-6x^2-210x+1,-6<= x<= 8
extreme
f
(
x
)
=
2
x
3
−
6
x
2
−
2
1
0
x
+
1
,
−
6
≤
x
≤
8
extreme f(x)=ln(x^2+3x+9)
extreme
f
(
x
)
=
ln
(
x
2
+
3
x
+
9
)
extreme f(x)=4x^2+x^2=2
extreme
f
(
x
)
=
4
x
2
+
x
2
=
2
extreme f(x)=((x-ln(x)))/x
extreme
f
(
x
)
=
(
x
−
ln
(
x
)
)
x
extreme f(x,y)=e^{10x^2+4y^2+2}
extreme
f
(
x
,
y
)
=
e
1
0
x
2
+
4
y
2
+
2
extreme f(x)=ln(x^2+3x+8)
extreme
f
(
x
)
=
ln
(
x
2
+
3
x
+
8
)
extreme f(x)=9sin(3x)
extreme
f
(
x
)
=
9
sin
(
3
x
)
extreme f(x,y)=16-8x+10y
extreme
f
(
x
,
y
)
=
1
6
−
8
x
+
1
0
y
extreme f(x)=20sin(2x)
extreme
f
(
x
)
=
2
0
sin
(
2
x
)
extreme x(3-x)
extreme
x
(
3
−
x
)
extreme f(x)=y*e^x+x*ln(y)
extreme
f
(
x
)
=
y
·
e
x
+
x
·
ln
(
y
)
extreme f(x)=(x^{(2/3)})(1-x^2)
extreme
f
(
x
)
=
(
x
(
2
3
)
)
(
1
−
x
2
)
extreme f(x,y)=(69120)/x+(69120)/y+5xy
extreme
f
(
x
,
y
)
=
6
9
1
2
0
x
+
6
9
1
2
0
y
+
5
xy
extreme f(x)=4x^2-8x+7y^2+8
extreme
f
(
x
)
=
4
x
2
−
8
x
+
7
y
2
+
8
extreme (2x-5)/(3\sqrt[3]{x)}+x^{2/3}
extreme
2
x
−
5
3
3
√
x
+
x
2
3
extreme f(x)=2(csc(x)+sec(x))
extreme
f
(
x
)
=
2
(
csc
(
x
)
+
sec
(
x
)
)
extreme f(x,y)=xe^y-ln(x)
extreme
f
(
x
,
y
)
=
xe
y
−
ln
(
x
)
extreme y= 5/x
extreme
y
=
5
x
extreme f(x)=x^4-x^2+2
extreme
f
(
x
)
=
x
4
−
x
2
+
2
extreme f(x)=(x^2-16)/(x-5)
extreme
f
(
x
)
=
x
2
−
1
6
x
−
5
extreme 15sin(5000pit)
extreme
1
5
sin
(
5
0
0
0
π
t
)
extreme x^4+2x^2+y^4-2y^2+3
extreme
x
4
+
2
x
2
+
y
4
−
2
y
2
+
3
extreme f(x)=9*x^3-7*x^2+3*x+10
extreme
f
(
x
)
=
9
·
x
3
−
7
·
x
2
+
3
·
x
+
1
0
extreme f(x)=x^2-6,-2<= x<= 4
extreme
f
(
x
)
=
x
2
−
6
,
−
2
≤
x
≤
4
extreme f(x,y)=e^{-2x^2-4y^2}
extreme
f
(
x
,
y
)
=
e
−
2
x
2
−
4
y
2
extreme 6x^2-48x-190
extreme
6
x
2
−
4
8
x
−
1
9
0
extreme f(x)=(e^x)/((4+e^x))
extreme
f
(
x
)
=
e
x
(
4
+
e
x
)
extreme f(x)=4x^3-2x^2-5
extreme
f
(
x
)
=
4
x
3
−
2
x
2
−
5
extreme T(x,y)=ln(3xy+2x^2-y)
extreme
T
(
x
,
y
)
=
ln
(
3
xy
+
2
x
2
−
y
)
extreme f(x)=5000-15x+0.08x^2
extreme
f
(
x
)
=
5
0
0
0
−
1
5
x
+
0
.
0
8
x
2
extreme 2y^2+2xy+x^2-16x-20y
extreme
2
y
2
+
2
xy
+
x
2
−
1
6
x
−
2
0
y
extreme f(x)=-2x^2+200x
extreme
f
(
x
)
=
−
2
x
2
+
2
0
0
x
extreme y=x^2-5x-14
extreme
y
=
x
2
−
5
x
−
1
4
extreme sqrt(x)*7-x
extreme
√
x
·
7
−
x
extreme f(x)=-5x^2-8y^2-2xy+102y
extreme
f
(
x
)
=
−
5
x
2
−
8
y
2
−
2
xy
+
1
0
2
y
extreme f(x)=x^{2/3},-1<= x<= 8
extreme
f
(
x
)
=
x
2
3
,
−
1
≤
x
≤
8
extreme 2x^3-3x^2-72x+1
extreme
2
x
3
−
3
x
2
−
7
2
x
+
1
extreme f(x)=\sqrt[3]{x(x^2-1)}
extreme
f
(
x
)
=
3
√
x
(
x
2
−
1
)
extreme f(x)=(x^5)/5-ln(x)
extreme
f
(
x
)
=
x
5
5
−
ln
(
x
)
extreme f(x,y)=8x^4-x^2+3y^2
extreme
f
(
x
,
y
)
=
8
x
4
−
x
2
+
3
y
2
extreme f(x,y)=3x^2+y^3-18xy+22
extreme
f
(
x
,
y
)
=
3
x
2
+
y
3
−
1
8
xy
+
2
2
extreme f(3.2)=-(40000t)/((3+t^2+2x^2)^2)
extreme
f
(
3
.
2
)
=
−
4
0
0
0
0
t
(
3
+
t
2
+
2
x
2
)
2
extreme (4e^{-2x})/(2x+5)
extreme
4
e
−
2
x
2
x
+
5
extreme f(x,y)=-2x^2-y^3+9y^2+16x-15y+5
extreme
f
(
x
,
y
)
=
−
2
x
2
−
y
3
+
9
y
2
+
1
6
x
−
1
5
y
+
5
extreme f(x)=2x^2+(91.2)/x
extreme
f
(
x
)
=
2
x
2
+
9
1
.
2
x
extreme P(a)=y^2-4r^2+r+e^2
extreme
P
(
a
)
=
y
2
−
4
r
2
+
r
+
e
2
extreme f(t)=25cos(2t)
extreme
f
(
t
)
=
2
5
cos
(
2
t
)
extreme f(x)=-2x^3+24x^2-42x+7
extreme
f
(
x
)
=
−
2
x
3
+
2
4
x
2
−
4
2
x
+
7
extreme f(x)=-0.01x^2+120x+200000
extreme
f
(
x
)
=
−
0
.
0
1
x
2
+
1
2
0
x
+
2
0
0
0
0
0
extreme f(xy)=-x^2-2y^2+xy+x+3y
extreme
f
(
xy
)
=
−
x
2
−
2
y
2
+
xy
+
x
+
3
y
extreme x/(ln(x^2))
extreme
x
ln
(
x
2
)
extreme x^{2x}
extreme
x
2
x
extreme f(x)=4xy^2+2xy-3y
extreme
f
(
x
)
=
4
xy
2
+
2
xy
−
3
y
extreme f(x,y)=(500)/((4+x^2+y^2))
extreme
f
(
x
,
y
)
=
5
0
0
(
4
+
x
2
+
y
2
)
extreme f(x)=(5+x)/(4-x)
extreme
f
(
x
)
=
5
+
x
4
−
x
extreme f(x)=7x^2+x-3
extreme
f
(
x
)
=
7
x
2
+
x
−
3
extreme y=5x+(180)/x
extreme
y
=
5
x
+
1
8
0
x
extreme (-8x^3+5x^2-1)/(2x^2-9x)
extreme
−
8
x
3
+
5
x
2
−
1
2
x
2
−
9
x
extreme f(x)=x-6sqrt(x+9)
extreme
f
(
x
)
=
x
−
6
√
x
+
9
extreme f(x)= x/(4x-x^3)
extreme
f
(
x
)
=
x
4
x
−
x
3
extreme x^2-10x-9,2<= x<= 7
extreme
x
2
−
1
0
x
−
9
,
2
≤
x
≤
7
extreme 0.002x^2+4.4x-90
extreme
0
.
0
0
2
x
2
+
4
.
4
x
−
9
0
extreme f(x)=7-4x^2
extreme
f
(
x
)
=
7
−
4
x
2
extreme f(x,y)=((1x+3y))/(1+x^2+y^2)
extreme
f
(
x
,
y
)
=
(
1
x
+
3
y
)
1
+
x
2
+
y
2
extreme sqrt(x^2+y^2-2x+26)
extreme
√
x
2
+
y
2
−
2
x
+
2
6
extreme f(x)=-1.25x^2+160x-2500
extreme
f
(
x
)
=
−
1
.
2
5
x
2
+
1
6
0
x
−
2
5
0
0
extreme f(x)=2x^3-150x+3
extreme
f
(
x
)
=
2
x
3
−
1
5
0
x
+
3
extreme f(x,y)=x^2+1/2 y^2+1/2 (y-x)-3/2
extreme
f
(
x
,
y
)
=
x
2
+
1
2
y
2
+
1
2
(
y
−
x
)
−
3
2
extreme x^4+3x^3+2x^2+x+1
extreme
x
4
+
3
x
3
+
2
x
2
+
x
+
1
extreme f(x)=-0.4x^2+90x-2000,0<= x
extreme
f
(
x
)
=
−
0
.
4
x
2
+
9
0
x
−
2
0
0
0
,
0
≤
x
extreme 2x^2-2x
extreme
2
x
2
−
2
x
extreme f(x)=(x-2)^{1/8}
extreme
f
(
x
)
=
(
x
−
2
)
1
8
extreme y=2cos(x)-11x+7[-pi,0]
extreme
y
=
2
cos
(
x
)
−
1
1
x
+
7
[
−
π
,
0
]
extreme y=(x^2-4)^4(x^2+1)^5
extreme
y
=
(
x
2
−
4
)
4
(
x
2
+
1
)
5
extreme f(x)=((x^2-2x+1))/(x+1)
extreme
f
(
x
)
=
(
x
2
−
2
x
+
1
)
x
+
1
extreme f(x)=-x^3+6x^2-9x-1
extreme
f
(
x
)
=
−
x
3
+
6
x
2
−
9
x
−
1
extreme f(x)=(-1/100 (x)(x-300))
extreme
f
(
x
)
=
(
−
1
1
0
0
(
x
)
(
x
−
3
0
0
)
)
extreme f(x)=2x+6,-4<= x<= 2
extreme
f
(
x
)
=
2
x
+
6
,
−
4
≤
x
≤
2
extreme f(x)=(x-9)^3
extreme
f
(
x
)
=
(
x
−
9
)
3
extreme f(x)=1-x^{4/5}
extreme
f
(
x
)
=
1
−
x
4
5
extreme f(x)=4+5x+x^2
extreme
f
(
x
)
=
4
+
5
x
+
x
2
extreme-2x+3ln(4x),1<= x<= 5
extreme
−
2
x
+
3
ln
(
4
x
)
,
1
≤
x
≤
5
extreme f(x)=((-x^6-5x^3+5x))/((x^2+2))
extreme
f
(
x
)
=
(
−
x
6
−
5
x
3
+
5
x
)
(
x
2
+
2
)
extreme f(x,y)=x^2+xy+y^2-9x+1
extreme
f
(
x
,
y
)
=
x
2
+
xy
+
y
2
−
9
x
+
1
extreme (4s)/(s^2-16)
extreme
4
s
s
2
−
1
6
extreme f(x,y)=sqrt(107-4x^2-3y^2)
extreme
f
(
x
,
y
)
=
√
1
0
7
−
4
x
2
−
3
y
2
1
..
829
830
831
832
833
..
839