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일반적인 Functions & Graphing 문제
extreme f(x)= 3/2 t^4-t^6
extreme
f
(
x
)
=
3
2
t
4
−
t
6
extreme f(x,y)=-x^2-y^3+3y^2-2x+45y+1
extreme
f
(
x
,
y
)
=
−
x
2
−
y
3
+
3
y
2
−
2
x
+
4
5
y
+
1
extreme y=-12x^5-45x^4+20x^3-1
extreme
y
=
−
1
2
x
5
−
4
5
x
4
+
2
0
x
3
−
1
extreme f(x)=x^3-2x-4x+4(0.3)
extreme
f
(
x
)
=
x
3
−
2
x
−
4
x
+
4
(
0
.
3
)
extreme x^2+x^{-2}
extreme
x
2
+
x
−
2
extreme (x-3)^2(x-2)
extreme
(
x
−
3
)
2
(
x
−
2
)
extreme f(x)=6x^2-6x+9
extreme
f
(
x
)
=
6
x
2
−
6
x
+
9
extreme f(x)=2y^2+2xy+x^2-16x-20y
extreme
f
(
x
)
=
2
y
2
+
2
xy
+
x
2
−
1
6
x
−
2
0
y
extreme-2/(4x+x^2-2)
extreme
−
2
4
x
+
x
2
−
2
extreme f(x)=4x^3+9x^2
extreme
f
(
x
)
=
4
x
3
+
9
x
2
extreme f(x,y)=x^2*y^2+x^2-x*y^2-5*x-7
extreme
f
(
x
,
y
)
=
x
2
·
y
2
+
x
2
−
x
·
y
2
−
5
·
x
−
7
extreme (3x)/(x-2)
extreme
3
x
x
−
2
extreme f(x,y)=8xy+1/x+1/y
extreme
f
(
x
,
y
)
=
8
xy
+
1
x
+
1
y
extreme f(x,y)=3xy-6x-3y+7
extreme
f
(
x
,
y
)
=
3
xy
−
6
x
−
3
y
+
7
extreme 5+6x-8x^3
extreme
5
+
6
x
−
8
x
3
extreme y=(t-3t^2)^{1/3}
extreme
y
=
(
t
−
3
t
2
)
1
3
extreme f(x)=Y(x)=-2x^3-3x^2+3x+3
extreme
f
(
x
)
=
Y
(
x
)
=
−
2
x
3
−
3
x
2
+
3
x
+
3
extreme f(1)=x^3-6x^2+9x+2
extreme
f
(
1
)
=
x
3
−
6
x
2
+
9
x
+
2
extreme f(x)= 2/3 x^3+11/2 x^2-21x+5
extreme
f
(
x
)
=
2
3
x
3
+
1
1
2
x
2
−
2
1
x
+
5
extreme f(x)=(x-3)e^{-5x}
extreme
f
(
x
)
=
(
x
−
3
)
e
−
5
x
extreme f(x)=-2^3-3*(-2^2)+3*(-2)+1
extreme
f
(
x
)
=
−
2
3
−
3
·
(
−
2
2
)
+
3
·
(
−
2
)
+
1
extreme g(x)=e^{-x^4},-3<= x<= 1
extreme
g
(
x
)
=
e
−
x
4
,
−
3
≤
x
≤
1
extreme f(x,y)=x^2+y^2-4x+3y
extreme
f
(
x
,
y
)
=
x
2
+
y
2
−
4
x
+
3
y
extreme f(x,y)=2^3-y^2+2xy+1
extreme
f
(
x
,
y
)
=
2
3
−
y
2
+
2
xy
+
1
extreme y=x^2+2
extreme
y
=
x
2
+
2
extreme f(x)=2^{(x+0.528)}-10(x+0.528)
extreme
f
(
x
)
=
2
(
x
+
0
.
5
2
8
)
−
1
0
(
x
+
0
.
5
2
8
)
extreme y=x^2-5
extreme
y
=
x
2
−
5
extreme-x^2-4x+1
extreme
−
x
2
−
4
x
+
1
extreme f(x)=3x^3-24x^2+48x-6
extreme
f
(
x
)
=
3
x
3
−
2
4
x
2
+
4
8
x
−
6
extreme 5/(x+1)
extreme
5
x
+
1
extreme f(x)=((x-1)^2)/(x^2-1)
extreme
f
(
x
)
=
(
x
−
1
)
2
x
2
−
1
extreme y=-(x-1)(x+2)^3
extreme
y
=
−
(
x
−
1
)
(
x
+
2
)
3
extreme x^4-4x^3+14
extreme
x
4
−
4
x
3
+
1
4
extreme f(x)=(2x^2+18)/x
extreme
f
(
x
)
=
2
x
2
+
1
8
x
extreme f(x)=-x^2-15.9x-57
extreme
f
(
x
)
=
−
x
2
−
1
5
.
9
x
−
5
7
extreme f(x,y)=x^2+y^2-4x+2y
extreme
f
(
x
,
y
)
=
x
2
+
y
2
−
4
x
+
2
y
extreme f(x)=(-x^2-10x-13)/(x+9)
extreme
f
(
x
)
=
−
x
2
−
1
0
x
−
1
3
x
+
9
extreme x^3-9x^2+1
extreme
x
3
−
9
x
2
+
1
extreme f(x)=(-24x^2-20x+24)/((x^2+1)^2)
extreme
f
(
x
)
=
−
2
4
x
2
−
2
0
x
+
2
4
(
x
2
+
1
)
2
extreme f(x)=x^2+y^2+20x-8y
extreme
f
(
x
)
=
x
2
+
y
2
+
2
0
x
−
8
y
extreme f(x)=x+y+8/(xy)
extreme
f
(
x
)
=
x
+
y
+
8
xy
extreme f(x)=-15051x^2+47796x+13402
extreme
f
(
x
)
=
−
1
5
0
5
1
x
2
+
4
7
7
9
6
x
+
1
3
4
0
2
extreme y=-3x^5+5x^3+1
extreme
y
=
−
3
x
5
+
5
x
3
+
1
extreme 5/(x+8)
extreme
5
x
+
8
extreme g(θ)=5θ-9sin(θ)
extreme
g
(
θ
)
=
5
θ
−
9
sin
(
θ
)
extreme f(x)=9-x,(-1,3)
extreme
f
(
x
)
=
9
−
x
,
(
−
1
,
3
)
extreme f(x)=4xsqrt(x-x^2)
extreme
f
(
x
)
=
4
x
√
x
−
x
2
extreme x^3+y^3-2xy
extreme
x
3
+
y
3
−
2
xy
extreme f(x,y)=x^3+y^3+6x^2-9y^2-4
extreme
f
(
x
,
y
)
=
x
3
+
y
3
+
6
x
2
−
9
y
2
−
4
extreme f(x)= 1/9 (x^4-4x^3)
extreme
f
(
x
)
=
1
9
(
x
4
−
4
x
3
)
extreme f(x)=x^3+2x^2-x-10
extreme
f
(
x
)
=
x
3
+
2
x
2
−
x
−
1
0
extreme f(x)=(x^3+1)/x
extreme
f
(
x
)
=
x
3
+
1
x
extreme f(x)=-2x^2+12x
extreme
f
(
x
)
=
−
2
x
2
+
1
2
x
extreme cos(x)-sin(x)
extreme
cos
(
x
)
−
sin
(
x
)
extreme f(x)=(1-x^2)/(x^2+1)
extreme
f
(
x
)
=
1
−
x
2
x
2
+
1
extreme 2t^2+7t+9
extreme
2
t
2
+
7
t
+
9
extreme f(x)=6xsqrt(16-x^2)
extreme
f
(
x
)
=
6
x
√
1
6
−
x
2
extreme f(x)=6x^2-40x+50
extreme
f
(
x
)
=
6
x
2
−
4
0
x
+
5
0
extreme y=(x^2+9)/(x^2-64)
extreme
y
=
x
2
+
9
x
2
−
6
4
extreme f(x)=5x+8y
extreme
f
(
x
)
=
5
x
+
8
y
extreme (cos(x))/(cos(2x))
extreme
cos
(
x
)
cos
(
2
x
)
extreme f(x)=((e^x)/(5+e^x))
extreme
f
(
x
)
=
(
e
x
5
+
e
x
)
extreme f(x,y)=-2x^2+2xy-2x
extreme
f
(
x
,
y
)
=
−
2
x
2
+
2
xy
−
2
x
extreme (180ln(x)-300)/(x^2)
extreme
1
8
0
ln
(
x
)
−
3
0
0
x
2
extreme f(x,y)=x^2+y^2-4
extreme
f
(
x
,
y
)
=
x
2
+
y
2
−
4
extreme f(x)=a+2b=53
extreme
f
(
x
)
=
a
+
2
b
=
5
3
extreme F(x,y)=x^3-4x^2-xy-y^2
extreme
F
(
x
,
y
)
=
x
3
−
4
x
2
−
xy
−
y
2
extreme f(x)=x^2-4x-7
extreme
f
(
x
)
=
x
2
−
4
x
−
7
extreme f(x,y)=4x^2-8y^2
extreme
f
(
x
,
y
)
=
4
x
2
−
8
y
2
extreme f(x)=5x+4y
extreme
f
(
x
)
=
5
x
+
4
y
extreme x^4-242x^2-2
extreme
x
4
−
2
4
2
x
2
−
2
extreme f(x)=x(20-2x)(32-2x),0<x<10
extreme
f
(
x
)
=
x
(
2
0
−
2
x
)
(
3
2
−
2
x
)
,
0
<
x
<
1
0
extreme f(x)=3|x-1|,0<x<3
extreme
f
(
x
)
=
3
|
x
−
1
|
,
0
<
x
<
3
extreme f(x)=(x+3)/(x^2-2x+1)
extreme
f
(
x
)
=
x
+
3
x
2
−
2
x
+
1
extreme f(x,y)=x^3+y^3+xy
extreme
f
(
x
,
y
)
=
x
3
+
y
3
+
xy
extreme f(x)=2+x^{2/5}
extreme
f
(
x
)
=
2
+
x
2
5
extreme x^2-4x+1
extreme
x
2
−
4
x
+
1
extreme f(x)=x 4/3 (x-4)
extreme
f
(
x
)
=
x
4
3
(
x
−
4
)
extreme f(x)=x^4-8x^2-6
extreme
f
(
x
)
=
x
4
−
8
x
2
−
6
extreme f(x)=x^4-8x^2-7
extreme
f
(
x
)
=
x
4
−
8
x
2
−
7
extreme f(x,y)=y^3+2y^2x+5yx^2-5y
extreme
f
(
x
,
y
)
=
y
3
+
2
y
2
x
+
5
yx
2
−
5
y
extreme h(v,t)=3vt-9t^2
extreme
h
(
v
,
t
)
=
3
vt
−
9
t
2
extreme f(x)=((2x-9))/x
extreme
f
(
x
)
=
(
2
x
−
9
)
x
extreme f(x,y)=400-9x^2-36y^2
extreme
f
(
x
,
y
)
=
4
0
0
−
9
x
2
−
3
6
y
2
extreme f(x)=(2-x)^2(0+x)
extreme
f
(
x
)
=
(
2
−
x
)
2
(
0
+
x
)
extreme f(x,y)=(-4x)/(x^2+y^2+1)
extreme
f
(
x
,
y
)
=
−
4
x
x
2
+
y
2
+
1
extreme f(x,y)=x^2-6x+10
extreme
f
(
x
,
y
)
=
x
2
−
6
x
+
1
0
extreme f(x)=(32x)/(x^2+16)
extreme
f
(
x
)
=
3
2
x
x
2
+
1
6
extreme 2x*e^{-x+1}+4
extreme
2
x
·
e
−
x
+
1
+
4
extreme f(x)=3x^3+y^3-9xy+27
extreme
f
(
x
)
=
3
x
3
+
y
3
−
9
xy
+
2
7
extreme f(x)=15+398x+184y-9x^2-2y^2-8xy
extreme
f
(
x
)
=
1
5
+
3
9
8
x
+
1
8
4
y
−
9
x
2
−
2
y
2
−
8
xy
extreme f(x)=cos(x),-pi/4 <= x<= pi/4
extreme
f
(
x
)
=
cos
(
x
)
,
−
π
4
≤
x
≤
π
4
extreme-3x^2-6x+3
extreme
−
3
x
2
−
6
x
+
3
extreme f(x)=xy+8/x
extreme
f
(
x
)
=
xy
+
8
x
extreme f(x,y)=x^{(2)}-2xy+4y^{(2)}-4x-2y+24
extreme
f
(
x
,
y
)
=
x
(
2
)
−
2
xy
+
4
y
(
2
)
−
4
x
−
2
y
+
2
4
extreme f(x)=(2+x)/(7-x),-7<= x<= 0
extreme
f
(
x
)
=
2
+
x
7
−
x
,
−
7
≤
x
≤
0
extreme y=3x^4+16x^3=x^3(3x+16)
extreme
y
=
3
x
4
+
1
6
x
3
=
x
3
(
3
x
+
1
6
)
extreme f(x)=-4x^3-6x^2+72x+6
extreme
f
(
x
)
=
−
4
x
3
−
6
x
2
+
7
2
x
+
6
extreme y=12x^{5/7}+5x^{12/7}
extreme
y
=
1
2
x
5
7
+
5
x
1
2
7
extreme y=x^3-3x^2+7x-10
extreme
y
=
x
3
−
3
x
2
+
7
x
−
1
0
1
..
832
833
834
835
836
..
839
