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일반적인 문제
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일반적인 Functions & Graphing 문제
extreme f(x)=(x^2-x+1)/(x^2-2x+2)
extreme
f
(
x
)
=
x
2
−
x
+
1
x
2
−
2
x
+
2
extreme f(x)=3+3x+x^2
extreme
f
(
x
)
=
3
+
3
x
+
x
2
extreme x/(ln(x)),2<= x<= 10
extreme
x
ln
(
x
)
,
2
≤
x
≤
1
0
extreme f(x)=10000e^{0.17(x-1.62)^2}
extreme
f
(
x
)
=
1
0
0
0
0
e
0
.
1
7
(
x
−
1
.
6
2
)
2
extreme f(x,y)=(5x)/(1+x^2+y^2)
extreme
f
(
x
,
y
)
=
5
x
1
+
x
2
+
y
2
extreme f(x)=x^3-4x+6
extreme
f
(
x
)
=
x
3
−
4
x
+
6
extreme f(x)=x^3-4x+3
extreme
f
(
x
)
=
x
3
−
4
x
+
3
extreme f(x)= x/2-3sin(x/3),0<= x<= 2pi
extreme
f
(
x
)
=
x
2
−
3
sin
(
x
3
)
,
0
≤
x
≤
2
π
extreme f(x,y)=sqrt(81-(x^2+y^2))
extreme
f
(
x
,
y
)
=
√
8
1
−
(
x
2
+
y
2
)
extreme f(x)=x^2+xy+y^2-12x+9
extreme
f
(
x
)
=
x
2
+
xy
+
y
2
−
1
2
x
+
9
extreme f(x)=5+(8+5x)^{2/5}
extreme
f
(
x
)
=
5
+
(
8
+
5
x
)
2
5
extreme f(x)=x^2y-2xy+2y^2x
extreme
f
(
x
)
=
x
2
y
−
2
xy
+
2
y
2
x
extreme f(x)=xe-4x^2
extreme
f
(
x
)
=
xe
−
4
x
2
extreme e^x+(1-x)/(e^x)
extreme
e
x
+
1
−
x
e
x
extreme y=f(x)=x(x-1)^5
extreme
y
=
f
(
x
)
=
x
(
x
−
1
)
5
extreme y=(e^{(2-x)}+x^2-x)/2
extreme
y
=
e
(
2
−
x
)
+
x
2
−
x
2
extreme f(x)=20(1+1/x+1/(x^2))
extreme
f
(
x
)
=
2
0
(
1
+
1
x
+
1
x
2
)
extreme 2x^2-2xy+y^2-2x
extreme
2
x
2
−
2
xy
+
y
2
−
2
x
extreme f(x)=(y-1)/(y^3-y+1)
extreme
f
(
x
)
=
y
−
1
y
3
−
y
+
1
extreme f(x,y)=2x^2+2y^2-16x+12y
extreme
f
(
x
,
y
)
=
2
x
2
+
2
y
2
−
1
6
x
+
1
2
y
extreme f(x)=x^3-15x^2+63x-15
extreme
f
(
x
)
=
x
3
−
1
5
x
2
+
6
3
x
−
1
5
extreme f(x,y)=(8460)/x+(8460)/y+5xy
extreme
f
(
x
,
y
)
=
8
4
6
0
x
+
8
4
6
0
y
+
5
xy
extreme f(x)=(85-0.05x)-(600+35x)
extreme
f
(
x
)
=
(
8
5
−
0
.
0
5
x
)
−
(
6
0
0
+
3
5
x
)
extreme f(x)=4x^2-24x+400
extreme
f
(
x
)
=
4
x
2
−
2
4
x
+
4
0
0
extreme f(x,y)=-5x^2-6y^2+5x-12y+5
extreme
f
(
x
,
y
)
=
−
5
x
2
−
6
y
2
+
5
x
−
1
2
y
+
5
extreme f(x)=-9+2x-x^2
extreme
f
(
x
)
=
−
9
+
2
x
−
x
2
extreme f(x,y)=2x^2+2y^2-16x+16y
extreme
f
(
x
,
y
)
=
2
x
2
+
2
y
2
−
1
6
x
+
1
6
y
extreme x^2(2+y^2)+yln(y)
extreme
x
2
(
2
+
y
2
)
+
y
ln
(
y
)
extreme 3x2+3y2+3z2+2y-2z=9
extreme
3
x
2
+
3
y
2
+
3
z
2
+
2
y
−
2
z
=
9
extreme f(x)=f(x)=3-3x^2
extreme
f
(
x
)
=
f
(
x
)
=
3
−
3
x
2
extreme f(x)=0.00324x^2-0.501x+33.684
extreme
f
(
x
)
=
0
.
0
0
3
2
4
x
2
−
0
.
5
0
1
x
+
3
3
.
6
8
4
extreme f(x,y)=(x-y)^2-x^4-y
extreme
f
(
x
,
y
)
=
(
x
−
y
)
2
−
x
4
−
y
extreme f(x)=x^3-x^2-x+9,-1<= x<= 2
extreme
f
(
x
)
=
x
3
−
x
2
−
x
+
9
,
−
1
≤
x
≤
2
extreme f(x,y)=x^2+y^2-2x+4y
extreme
f
(
x
,
y
)
=
x
2
+
y
2
−
2
x
+
4
y
단순화 r-s-1
simplify
r
−
s
−
1
extreme w(x,y)=xe^2y+e-y
extreme
w
(
x
,
y
)
=
xe
2
y
+
e
−
y
extreme f(x)=-2x^2+64x-80
extreme
f
(
x
)
=
−
2
x
2
+
6
4
x
−
8
0
extreme f(x,y)=sqrt(x^2+y^2+6x+10)
extreme
f
(
x
,
y
)
=
√
x
2
+
y
2
+
6
x
+
1
0
extreme f(x)=-34.3x^2+460.2x
extreme
f
(
x
)
=
−
3
4
.
3
x
2
+
4
6
0
.
2
x
extreme f(x)=-3(5-3x)e^{-4x},(-1,4)
extreme
f
(
x
)
=
−
3
(
5
−
3
x
)
e
−
4
x
,
(
−
1
,
4
)
extreme f(x)=x^3-6x^2+18
extreme
f
(
x
)
=
x
3
−
6
x
2
+
1
8
extreme f(x)=4x+8/x
extreme
f
(
x
)
=
4
x
+
8
x
extreme f(x)=-x^2+229x
extreme
f
(
x
)
=
−
x
2
+
2
2
9
x
extreme f(x)=6x-0.2x^2,0<= x<= 30
extreme
f
(
x
)
=
6
x
−
0
.
2
x
2
,
0
≤
x
≤
3
0
extreme 5x^5-3x^4+2
extreme
5
x
5
−
3
x
4
+
2
extreme f(x)=4-x,-3<= x<= 3
extreme
f
(
x
)
=
4
−
x
,
−
3
≤
x
≤
3
extreme f(x,y)=(x^2-9)^2+(y^2-36)^2
extreme
f
(
x
,
y
)
=
(
x
2
−
9
)
2
+
(
y
2
−
3
6
)
2
extreme f(x)=-3x^2-12x+24y^2+12y=0
extreme
f
(
x
)
=
−
3
x
2
−
1
2
x
+
2
4
y
2
+
1
2
y
=
0
extreme f(x)=7x-5
extreme
f
(
x
)
=
7
x
−
5
extreme ln(x)-7x+11
extreme
ln
(
x
)
−
7
x
+
1
1
extreme f(x,y)=3-x^2-y^2+6y
extreme
f
(
x
,
y
)
=
3
−
x
2
−
y
2
+
6
y
extreme f(x)=sqrt(1-1)
extreme
f
(
x
)
=
√
1
−
1
extreme (x+1)^2-7
extreme
(
x
+
1
)
2
−
7
extreme f(x,y)=xy(1-5x-10y)
extreme
f
(
x
,
y
)
=
xy
(
1
−
5
x
−
1
0
y
)
extreme f(x)=x^2+y^2+18x-6y
extreme
f
(
x
)
=
x
2
+
y
2
+
1
8
x
−
6
y
extreme f(x)=100x+100y-x^2-y^2
extreme
f
(
x
)
=
1
0
0
x
+
1
0
0
y
−
x
2
−
y
2
extreme f(x)=x^2+y^2+18x-4y
extreme
f
(
x
)
=
x
2
+
y
2
+
1
8
x
−
4
y
extreme f(x)=x^3-9x^2,-1<= x<= 7
extreme
f
(
x
)
=
x
3
−
9
x
2
,
−
1
≤
x
≤
7
extreme f(x,y)=sqrt(x^2+y^2+9)
extreme
f
(
x
,
y
)
=
√
x
2
+
y
2
+
9
extreme f(x,y)=sqrt(x^2+y^2-2x+2)
extreme
f
(
x
,
y
)
=
√
x
2
+
y
2
−
2
x
+
2
extreme f(x)=2+9x+3x^2-x^3,-2<= x<= 6
extreme
f
(
x
)
=
2
+
9
x
+
3
x
2
−
x
3
,
−
2
≤
x
≤
6
extreme f(x,y)=2x^2+3y^2-4x-6y+19
extreme
f
(
x
,
y
)
=
2
x
2
+
3
y
2
−
4
x
−
6
y
+
1
9
extreme f(x)=x^3-24x^2+135x
extreme
f
(
x
)
=
x
3
−
2
4
x
2
+
1
3
5
x
extreme f(x)=x^3+y^3-30xy
extreme
f
(
x
)
=
x
3
+
y
3
−
3
0
xy
extreme (x^2+4x+3)/((x+2)^2)
extreme
x
2
+
4
x
+
3
(
x
+
2
)
2
extreme f(x)=3+3x^2-2x^3
extreme
f
(
x
)
=
3
+
3
x
2
−
2
x
3
extreme f(x)=x^4-72x+5
extreme
f
(
x
)
=
x
4
−
7
2
x
+
5
extreme f(x,y)=3e^{x^2+y^2}
extreme
f
(
x
,
y
)
=
3
e
x
2
+
y
2
extreme f(x,y)=(x-y)(2x+y)(x+1)
extreme
f
(
x
,
y
)
=
(
x
−
y
)
(
2
x
+
y
)
(
x
+
1
)
extreme f(xy)=2x^2+2xy+y^2+2x-3
extreme
f
(
xy
)
=
2
x
2
+
2
xy
+
y
2
+
2
x
−
3
extreme 2x^2+9
extreme
2
x
2
+
9
extreme y=2x^4-12x^2
extreme
y
=
2
x
4
−
1
2
x
2
extreme f(x)=(x^2+2)/(x^2+3)
extreme
f
(
x
)
=
x
2
+
2
x
2
+
3
extreme-x^2-x+1
extreme
−
x
2
−
x
+
1
extreme (x^2+x)/(|x|+1)
extreme
x
2
+
x
|
x
|
+
1
extreme 18xy-3x^2y-2xy^2
extreme
1
8
xy
−
3
x
2
y
−
2
xy
2
extreme f(x)=x^2-8x-9,1<= x<= 6
extreme
f
(
x
)
=
x
2
−
8
x
−
9
,
1
≤
x
≤
6
extreme f(x,y)=(y^2-4)(x-x^2)
extreme
f
(
x
,
y
)
=
(
y
2
−
4
)
(
x
−
x
2
)
extreme f(x)=x^2-8x+19
extreme
f
(
x
)
=
x
2
−
8
x
+
1
9
extreme f(x)=-0.02x^2+4x-40
extreme
f
(
x
)
=
−
0
.
0
2
x
2
+
4
x
−
4
0
extreme f(x,y)=2x^3+y^3+3x^2-3y^2-16
extreme
f
(
x
,
y
)
=
2
x
3
+
y
3
+
3
x
2
−
3
y
2
−
1
6
extreme f(x,y)=x^2-y^2+x+y+5
extreme
f
(
x
,
y
)
=
x
2
−
y
2
+
x
+
y
+
5
extreme f(x)=-x^2-x+1
extreme
f
(
x
)
=
−
x
2
−
x
+
1
extreme f(x,y)=5x^2+3xy+10y^2+4xy^2+6x^2y
extreme
f
(
x
,
y
)
=
5
x
2
+
3
xy
+
1
0
y
2
+
4
xy
2
+
6
x
2
y
extreme f(x)=8(xy)-2x^4-2y^4
extreme
f
(
x
)
=
8
(
xy
)
−
2
x
4
−
2
y
4
extreme f(x)=3x^3+3x^2-10x-2
extreme
f
(
x
)
=
3
x
3
+
3
x
2
−
1
0
x
−
2
extreme f(x)=0.0001x^2+3.2x-90
extreme
f
(
x
)
=
0
.
0
0
0
1
x
2
+
3
.
2
x
−
9
0
extreme f(x,y)=θ
extreme
f
(
x
,
y
)
=
θ
extreme (x^3)/3-x^2-35x+4
extreme
x
3
3
−
x
2
−
3
5
x
+
4
extreme f(x,y)=e^{6x^2+4y^2+10}
extreme
f
(
x
,
y
)
=
e
6
x
2
+
4
y
2
+
1
0
extreme f(x,y)=xy-8x-y^2+12x+160
extreme
f
(
x
,
y
)
=
xy
−
8
x
−
y
2
+
1
2
x
+
1
6
0
extreme f(x,y)=x^2+3y^2-y^3-4x
extreme
f
(
x
,
y
)
=
x
2
+
3
y
2
−
y
3
−
4
x
extreme f(x)=0.4x^2+110.2x,0<= x
extreme
f
(
x
)
=
0
.
4
x
2
+
1
1
0
.
2
x
,
0
≤
x
extreme f(x)=((3x))/((9-x^2)),-3<= x<= 2
extreme
f
(
x
)
=
(
3
x
)
(
9
−
x
2
)
,
−
3
≤
x
≤
2
extreme f(x)= 1/4 x+1/x ,x>0
extreme
f
(
x
)
=
1
4
x
+
1
x
,
x
>
0
extreme f(0)=x^2-4x-4
extreme
f
(
0
)
=
x
2
−
4
x
−
4
extreme (7e^x+7e^{-x})/2
extreme
7
e
x
+
7
e
−
x
2
extreme f(x)=x^3+x^2-12
extreme
f
(
x
)
=
x
3
+
x
2
−
1
2
extreme f(x)=x^4-72x^2+1296,-7<= x<= 7
extreme
f
(
x
)
=
x
4
−
7
2
x
2
+
1
2
9
6
,
−
7
≤
x
≤
7
extreme f(x)=e^{-at}
extreme
f
(
x
)
=
e
−
at
1
..
830
831
832
833
834
..
839
