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일반적인 Functions & Graphing 문제
extreme f(x)=2x^3+y^3+3x^2-3y-12x-4
extreme
f
(
x
)
=
2
x
3
+
y
3
+
3
x
2
−
3
y
−
1
2
x
−
4
extreme f(x)=(2x)/(x^2+4),-4<= x<= 4
extreme
f
(
x
)
=
2
x
x
2
+
4
,
−
4
≤
x
≤
4
extreme (5x)/(x^2-9)
extreme
5
x
x
2
−
9
extreme 3x^2+24x+45
extreme
3
x
2
+
2
4
x
+
4
5
extreme f(x)=(e^x)/(x^7)
extreme
f
(
x
)
=
e
x
x
7
extreme f(x)=7x^4-2x^2-8x+8
extreme
f
(
x
)
=
7
x
4
−
2
x
2
−
8
x
+
8
extreme f(x)=(x^3)/(-x^2+4)
extreme
f
(
x
)
=
x
3
−
x
2
+
4
extreme f(x)=((x^2-63))/(x-8)
extreme
f
(
x
)
=
(
x
2
−
6
3
)
x
−
8
extreme x^3+8y^3-6xy+5
extreme
x
3
+
8
y
3
−
6
xy
+
5
extreme f(x)=4x^3-60x^2+200x
extreme
f
(
x
)
=
4
x
3
−
6
0
x
2
+
2
0
0
x
extreme f(x)=x^3+2y^2+3xy+8
extreme
f
(
x
)
=
x
3
+
2
y
2
+
3
xy
+
8
extreme f(x,y)=x^2+xy+y^2-6x-9y
extreme
f
(
x
,
y
)
=
x
2
+
xy
+
y
2
−
6
x
−
9
y
extreme (x+3)/(x+2)
extreme
x
+
3
x
+
2
extreme f(x)=x(sqrt((39900-x)/5))
extreme
f
(
x
)
=
x
(
√
3
9
9
0
0
−
x
5
)
extreme f(x)=x^3-x^2-x+5,-1<= x<= 2
extreme
f
(
x
)
=
x
3
−
x
2
−
x
+
5
,
−
1
≤
x
≤
2
extreme f(x)=24x-24x^2+6x^3
extreme
f
(
x
)
=
2
4
x
−
2
4
x
2
+
6
x
3
extreme f(x)=-2x^2-4x+3
extreme
f
(
x
)
=
−
2
x
2
−
4
x
+
3
extreme f(x)=x^2log_{9}(x)
extreme
f
(
x
)
=
x
2
log
9
(
x
)
extreme f(x)=2000+530(ln(x))
extreme
f
(
x
)
=
2
0
0
0
+
5
3
0
(
ln
(
x
)
)
extreme f(x)=(3x+4)/(6x+1)
extreme
f
(
x
)
=
3
x
+
4
6
x
+
1
extreme f(x)=3x^4-96x^2+1
extreme
f
(
x
)
=
3
x
4
−
9
6
x
2
+
1
extreme f(x)=0.003x^2+4.2x-50
extreme
f
(
x
)
=
0
.
0
0
3
x
2
+
4
.
2
x
−
5
0
extreme f(x)=-3x^2+1
extreme
f
(
x
)
=
−
3
x
2
+
1
extreme f(x)=-3x^2+3
extreme
f
(
x
)
=
−
3
x
2
+
3
extreme f(x)=2x^3+x^2-20x
extreme
f
(
x
)
=
2
x
3
+
x
2
−
2
0
x
extreme f(x)=2x^2-4x[0.3]
extreme
f
(
x
)
=
2
x
2
−
4
x
[
0
.
3
]
extreme f(xy)=4x+8y
extreme
f
(
xy
)
=
4
x
+
8
y
extreme 5sin(3x)-5
extreme
5
sin
(
3
x
)
−
5
extreme f(x,y)=3x^2y+4xy-2
extreme
f
(
x
,
y
)
=
3
x
2
y
+
4
xy
−
2
extreme 1/2 (5x-3)
extreme
1
2
(
5
x
−
3
)
extreme f(x)=(3x^2+6)^2
extreme
f
(
x
)
=
(
3
x
2
+
6
)
2
extreme f(x,y)=x^2+4xy+5y^2-7x+9y-10
extreme
f
(
x
,
y
)
=
x
2
+
4
xy
+
5
y
2
−
7
x
+
9
y
−
1
0
extreme f(x)=9x-18cos(x),-2<= x<= 0
extreme
f
(
x
)
=
9
x
−
1
8
cos
(
x
)
,
−
2
≤
x
≤
0
extreme f(x)=2x^2-4x,0<= x<= 3
extreme
f
(
x
)
=
2
x
2
−
4
x
,
0
≤
x
≤
3
extreme x^2-18x+79
extreme
x
2
−
1
8
x
+
7
9
extreme f(x)=3x^4-294x^2+3,-8<= x<= 8
extreme
f
(
x
)
=
3
x
4
−
2
9
4
x
2
+
3
,
−
8
≤
x
≤
8
extreme f(x)=2x^2-7,-7<= x<= 7
extreme
f
(
x
)
=
2
x
2
−
7
,
−
7
≤
x
≤
7
extreme x^2-18x+86
extreme
x
2
−
1
8
x
+
8
6
extreme 2x^2-4x+6
extreme
2
x
2
−
4
x
+
6
extreme f(x)=3(x-e^x)
extreme
f
(
x
)
=
3
(
x
−
e
x
)
extreme f(x)=x^3+2x^2-4x+7
extreme
f
(
x
)
=
x
3
+
2
x
2
−
4
x
+
7
extreme f(x,y)=-4xy+2x^2-10y^2-4y^3-1
extreme
f
(
x
,
y
)
=
−
4
xy
+
2
x
2
−
1
0
y
2
−
4
y
3
−
1
extreme 4sin(2x),-2pi<= x<= pi
extreme
4
sin
(
2
x
)
,
−
2
π
≤
x
≤
π
extreme 0.3x^2-66x+15239
extreme
0
.
3
x
2
−
6
6
x
+
1
5
2
3
9
extreme a(-6-0)^2
extreme
a
(
−
6
−
0
)
2
extreme f(x,y)=2xy-(x^2y)/3-(2xy^2)/3
extreme
f
(
x
,
y
)
=
2
xy
−
x
2
y
3
−
2
xy
2
3
extreme f(x)=4sec(x)
extreme
f
(
x
)
=
4
sec
(
x
)
extreme f(x,y)=yx^2-3xye^{-xy}
extreme
f
(
x
,
y
)
=
yx
2
−
3
xye
−
xy
extreme f(x,y)=x^3-9xy-4y^2
extreme
f
(
x
,
y
)
=
x
3
−
9
xy
−
4
y
2
extreme y=4-6x^2
extreme
y
=
4
−
6
x
2
extreme (x^2+2)/(x-3)
extreme
x
2
+
2
x
−
3
extreme f(x)=5+(48)/x+3x^2
extreme
f
(
x
)
=
5
+
4
8
x
+
3
x
2
extreme E(x,y)=15xy-22xy
extreme
E
(
x
,
y
)
=
1
5
xy
−
2
2
xy
extreme f(x)=4(x-4)^{2/3}
extreme
f
(
x
)
=
4
(
x
−
4
)
2
3
extreme f(x)=2x^2+16x-5
extreme
f
(
x
)
=
2
x
2
+
1
6
x
−
5
extreme f(x)=x(x-1)^5
extreme
f
(
x
)
=
x
(
x
−
1
)
5
extreme 2x^2-30x^2+54x+2
extreme
2
x
2
−
3
0
x
2
+
5
4
x
+
2
extreme y=(x-6)ln(x-6)
extreme
y
=
(
x
−
6
)
ln
(
x
−
6
)
extreme f(x,y)=(2y^2+x^2)e^{-(x^2+y^2-3)}
extreme
f
(
x
,
y
)
=
(
2
y
2
+
x
2
)
e
−
(
x
2
+
y
2
−
3
)
extreme p(x)=12x^4-62x^3+ax^2-98x+30
extreme
p
(
x
)
=
1
2
x
4
−
6
2
x
3
+
ax
2
−
9
8
x
+
3
0
extreme y=3z^2-3x^2
extreme
y
=
3
z
2
−
3
x
2
extreme 4-y^3-x^2-3xy
extreme
4
−
y
3
−
x
2
−
3
xy
extreme (10x^3-2)/(2x^3+5x^2+9x)
extreme
1
0
x
3
−
2
2
x
3
+
5
x
2
+
9
x
extreme-6x^2+336x-4320
extreme
−
6
x
2
+
3
3
6
x
−
4
3
2
0
extreme y=\sqrt[3]{x}+1/(\sqrt[3]{x)}
extreme
y
=
3
√
x
+
1
3
√
x
extreme f(x)=(12x)/(3.5x^2+2.5)
extreme
f
(
x
)
=
1
2
x
3
.
5
x
2
+
2
.
5
extreme f(y)=14x^2-2x^3+2y^2+4xy
extreme
f
(
y
)
=
1
4
x
2
−
2
x
3
+
2
y
2
+
4
xy
extreme f(x)=x(152-x)
extreme
f
(
x
)
=
x
(
1
5
2
−
x
)
extreme f(x,y)=7x^2y+9xy^2
extreme
f
(
x
,
y
)
=
7
x
2
y
+
9
xy
2
extreme f(x)=x^2+xy+y^2+2x-2y+6
extreme
f
(
x
)
=
x
2
+
xy
+
y
2
+
2
x
−
2
y
+
6
extreme f(x)=165000x-100x^2
extreme
f
(
x
)
=
1
6
5
0
0
0
x
−
1
0
0
x
2
extreme x/(x^2+81)
extreme
x
x
2
+
8
1
extreme f(x)= 1/(sqrt(2pi))e^{(-x^2)/2}
extreme
f
(
x
)
=
1
√
2
π
e
−
x
2
2
extreme f(x)=(2x)/(x^2+16),-5<= x<= 5
extreme
f
(
x
)
=
2
x
x
2
+
1
6
,
−
5
≤
x
≤
5
extreme f(x)=(3+x)/(7-x),-7<= x<= 0
extreme
f
(
x
)
=
3
+
x
7
−
x
,
−
7
≤
x
≤
0
extreme f(x)=e^{6x^2+4y^2+10}
extreme
f
(
x
)
=
e
6
x
2
+
4
y
2
+
1
0
extreme f(x,y)=(x^2-y^2)e^{-(x^2+y^2)}
extreme
f
(
x
,
y
)
=
(
x
2
−
y
2
)
e
−
(
x
2
+
y
2
)
extreme f(x)=x(x+3)e^{-2x}
extreme
f
(
x
)
=
x
(
x
+
3
)
e
−
2
x
extreme f(x)=-45x^2+400x
extreme
f
(
x
)
=
−
4
5
x
2
+
4
0
0
x
extreme f(x)=3x^2-2x+5
extreme
f
(
x
)
=
3
x
2
−
2
x
+
5
extreme f(x)=((2x^2+4x))/((2+x^2))
extreme
f
(
x
)
=
(
2
x
2
+
4
x
)
(
2
+
x
2
)
extreme f(x)=x^3+8x+12
extreme
f
(
x
)
=
x
3
+
8
x
+
1
2
extreme 7-6x-x^3
extreme
7
−
6
x
−
x
3
extreme f(x)=x(e^{-x/3})
extreme
f
(
x
)
=
x
(
e
−
x
3
)
extreme f(x)=x^2-14x+4
extreme
f
(
x
)
=
x
2
−
1
4
x
+
4
extreme f(x)=x^2-14x+6
extreme
f
(
x
)
=
x
2
−
1
4
x
+
6
extreme f(x,y)=x^3+3xy+y^3+k
extreme
f
(
x
,
y
)
=
x
3
+
3
xy
+
y
3
+
k
extreme f(x)=5+5x-5x^2,0<= x<= 3
extreme
f
(
x
)
=
5
+
5
x
−
5
x
2
,
0
≤
x
≤
3
extreme f(x)=-2x^2-x+4
extreme
f
(
x
)
=
−
2
x
2
−
x
+
4
extreme y=1250sin(2x)
extreme
y
=
1
2
5
0
sin
(
2
x
)
extreme f(x,y)=e^{2y-x^2-y^2}
extreme
f
(
x
,
y
)
=
e
2
y
−
x
2
−
y
2
extreme f(x,y)=x^2(x+y)+6xy
extreme
f
(
x
,
y
)
=
x
2
(
x
+
y
)
+
6
xy
extreme f(x)=-4x^3+12x^2-10
extreme
f
(
x
)
=
−
4
x
3
+
1
2
x
2
−
1
0
extreme f(x)=2x+7ln(x)
extreme
f
(
x
)
=
2
x
+
7
ln
(
x
)
extreme 68-11
extreme
6
8
−
1
1
monotone f(x)=x^3-75x+3
monotone
f
(
x
)
=
x
3
−
7
5
x
+
3
대칭 y=(x-5)^2-4
symmetry
y
=
(
x
−
5
)
2
−
4
extreme-(x+1)(x-1)^2
extreme
−
(
x
+
1
)
(
x
−
1
)
2
endbehavior f(x)=-(x-1)(x+2)(x+1)^2
endbehavior
f
(
x
)
=
−
(
x
−
1
)
(
x
+
2
)
(
x
+
1
)
2
가로채기 x
intercepts
x
1
..
834
835
836
837
838
839
