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일반적인 Functions & Graphing 문제
extreme f(x,y)=3x^2-2xy+y^2-8y
extreme
f
(
x
,
y
)
=
3
x
2
−
2
xy
+
y
2
−
8
y
extreme f(x)=-5x+3ln(4x)
extreme
f
(
x
)
=
−
5
x
+
3
ln
(
4
x
)
extreme f(x)=(3x)/(x^2+1)
extreme
f
(
x
)
=
3
x
x
2
+
1
extreme f(x)=(x^3+8)/x
extreme
f
(
x
)
=
x
3
+
8
x
extreme f(x)=x^3-9/2 x^2+1
extreme
f
(
x
)
=
x
3
−
9
2
x
2
+
1
extreme y=2x^2+z^2
extreme
y
=
2
x
2
+
z
2
extreme f(x,y)=1-3x^4-6x^2y+2y^3
extreme
f
(
x
,
y
)
=
1
−
3
x
4
−
6
x
2
y
+
2
y
3
extreme f(x)=8x^3+13x
extreme
f
(
x
)
=
8
x
3
+
1
3
x
extreme 2(1/2)^x
extreme
2
(
1
2
)
x
extreme f(x)=((x-4)^2)/(x+10)
extreme
f
(
x
)
=
(
x
−
4
)
2
x
+
1
0
extreme f(x)=4x-1
extreme
f
(
x
)
=
4
x
−
1
extreme f(x)=2y^2+x^2-x^2y
extreme
f
(
x
)
=
2
y
2
+
x
2
−
x
2
y
extreme f(x)= x/(x^2+100)
extreme
f
(
x
)
=
x
x
2
+
1
0
0
extreme f(x)=4x-9x^{4/9}
extreme
f
(
x
)
=
4
x
−
9
x
4
9
extreme f(x,y)=3x^3-9x+9xy^2
extreme
f
(
x
,
y
)
=
3
x
3
−
9
x
+
9
xy
2
extreme f(x)=2x^2-8x+y^2-8y+2
extreme
f
(
x
)
=
2
x
2
−
8
x
+
y
2
−
8
y
+
2
extreme f(x,y)=6x+3y-7
extreme
f
(
x
,
y
)
=
6
x
+
3
y
−
7
extreme-2x^2+3x-1
extreme
−
2
x
2
+
3
x
−
1
extreme f(x,y)=2x^3-y^2+2xy+1
extreme
f
(
x
,
y
)
=
2
x
3
−
y
2
+
2
xy
+
1
extreme f(x,y)=sqrt(1-xy)
extreme
f
(
x
,
y
)
=
√
1
−
xy
extreme f(x)= 1/7 x^7-x
extreme
f
(
x
)
=
1
7
x
7
−
x
extreme f(x,y)= 1/x+xy-8/y
extreme
f
(
x
,
y
)
=
1
x
+
xy
−
8
y
extreme f(x)=e^{xy}-x
extreme
f
(
x
)
=
e
xy
−
x
extreme y=3x^2-12x+13
extreme
y
=
3
x
2
−
1
2
x
+
1
3
extreme f(x)= 1/4 x^4-2x^3+3
extreme
f
(
x
)
=
1
4
x
4
−
2
x
3
+
3
extreme f(x)=((-8x^3+3x^2))/4
extreme
f
(
x
)
=
(
−
8
x
3
+
3
x
2
)
4
extreme f(x)=2x^3+x^2-4x+4
extreme
f
(
x
)
=
2
x
3
+
x
2
−
4
x
+
4
extreme f(x,y)=y(e^x-1)
extreme
f
(
x
,
y
)
=
y
(
e
x
−
1
)
extreme f(x)= x/(x^2+9),-4<= x<= 5
extreme
f
(
x
)
=
x
x
2
+
9
,
−
4
≤
x
≤
5
extreme x^3+3x^2-24x
extreme
x
3
+
3
x
2
−
2
4
x
extreme-x^3+4xy-2y^2+1
extreme
−
x
3
+
4
xy
−
2
y
2
+
1
extreme f(x)=-x^3+12x,(-6,5)
extreme
f
(
x
)
=
−
x
3
+
1
2
x
,
(
−
6
,
5
)
extreme f(x,y)=6-x^4+2x^2-y^2
extreme
f
(
x
,
y
)
=
6
−
x
4
+
2
x
2
−
y
2
extreme f(x,y)=8y^2+x^2-x^2y
extreme
f
(
x
,
y
)
=
8
y
2
+
x
2
−
x
2
y
extreme f(x)=2-3x^2
extreme
f
(
x
)
=
2
−
3
x
2
extreme f(x)=x-8\sqrt[3]{x}
extreme
f
(
x
)
=
x
−
8
3
√
x
extreme f(x)=2x^3-15x^2+36x+10
extreme
f
(
x
)
=
2
x
3
−
1
5
x
2
+
3
6
x
+
1
0
extreme f(x)=x^3-12x^2+45x+5
extreme
f
(
x
)
=
x
3
−
1
2
x
2
+
4
5
x
+
5
extreme f(x)=-x^{5/3}+5\sqrt[3]{x}
extreme
f
(
x
)
=
−
x
5
3
+
5
3
√
x
extreme f(x)=e^{-ax}
extreme
f
(
x
)
=
e
−
ax
extreme f(x)=-x^3+6x^2-9x
extreme
f
(
x
)
=
−
x
3
+
6
x
2
−
9
x
extreme f(x)=x^2+9x+5
extreme
f
(
x
)
=
x
2
+
9
x
+
5
extreme 7*8^{x+8}+6
extreme
7
·
8
x
+
8
+
6
extreme f(x,y)=x^3+y^2-12x-2y
extreme
f
(
x
,
y
)
=
x
3
+
y
2
−
1
2
x
−
2
y
extreme f(x)=sqrt(x^2+81)
extreme
f
(
x
)
=
√
x
2
+
8
1
extreme f(x)=5x-4ln(4x)
extreme
f
(
x
)
=
5
x
−
4
ln
(
4
x
)
extreme f(x)=x^4-3x^2=x^2(x^2-3)
extreme
f
(
x
)
=
x
4
−
3
x
2
=
x
2
(
x
2
−
3
)
extreme g(x,y)=x^3+y^3-3x-3y
extreme
g
(
x
,
y
)
=
x
3
+
y
3
−
3
x
−
3
y
extreme f(x)=-x^6-3x^3+x+1
extreme
f
(
x
)
=
−
x
6
−
3
x
3
+
x
+
1
x^2=-4ay
x
2
=
−
4
ay
extreme f(x)=3sin(x)cos(x)
extreme
f
(
x
)
=
3
sin
(
x
)
cos
(
x
)
extreme f(x)=4x-y
extreme
f
(
x
)
=
4
x
−
y
extreme f(x)=3sin(x)+3cos(x)
extreme
f
(
x
)
=
3
sin
(
x
)
+
3
cos
(
x
)
extreme (x^2)/(1-x^2)
extreme
x
2
1
−
x
2
extreme f(x)=(x+2)^{4/3},-6<= x<= 6
extreme
f
(
x
)
=
(
x
+
2
)
4
3
,
−
6
≤
x
≤
6
extreme f(x)=-x^3+15x^2
extreme
f
(
x
)
=
−
x
3
+
1
5
x
2
extreme f(x)=(x^2-14x+49)/(x-10)
extreme
f
(
x
)
=
x
2
−
1
4
x
+
4
9
x
−
1
0
extreme f(x)=e^{x^3-12x}
extreme
f
(
x
)
=
e
x
3
−
1
2
x
extreme (x-8x^2)^{1/3}
extreme
(
x
−
8
x
2
)
1
3
extreme x^2+8x+18
extreme
x
2
+
8
x
+
1
8
extreme f(x)=xe^{-x/2}
extreme
f
(
x
)
=
xe
−
x
2
extreme sqrt(1-x)+sqrt(1+x)+2sqrt(x)
extreme
√
1
−
x
+
√
1
+
x
+
2
√
x
extreme f(x)=xe^{-x/3}
extreme
f
(
x
)
=
xe
−
x
3
extreme f(x)=x^3+y^3-3x^2-3y^2-9x
extreme
f
(
x
)
=
x
3
+
y
3
−
3
x
2
−
3
y
2
−
9
x
extreme f(x)=2x^3-36x^2+210x-15
extreme
f
(
x
)
=
2
x
3
−
3
6
x
2
+
2
1
0
x
−
1
5
extreme f(x)=-4cos(3x)-4
extreme
f
(
x
)
=
−
4
cos
(
3
x
)
−
4
extreme f(x,y)=200y^2+x^2-x^2y
extreme
f
(
x
,
y
)
=
2
0
0
y
2
+
x
2
−
x
2
y
extreme 2x^4-16x^2+3
extreme
2
x
4
−
1
6
x
2
+
3
extreme f(x)= 2/3 x^3+2x^2+6x-5
extreme
f
(
x
)
=
2
3
x
3
+
2
x
2
+
6
x
−
5
extreme f(x,y)=x^2y-xy+3y^2
extreme
f
(
x
,
y
)
=
x
2
y
−
xy
+
3
y
2
extreme f(x)=2cos^2(x)
extreme
f
(
x
)
=
2
cos
2
(
x
)
extreme 6x^{2/3}-4x
extreme
6
x
2
3
−
4
x
extreme f(x)=4x^2+2y^2-2xy-10y-2x
extreme
f
(
x
)
=
4
x
2
+
2
y
2
−
2
xy
−
1
0
y
−
2
x
extreme f(x)=2x^2-6x^4
extreme
f
(
x
)
=
2
x
2
−
6
x
4
extreme f(x)=-x^2+10,-3<= x<= 4
extreme
f
(
x
)
=
−
x
2
+
1
0
,
−
3
≤
x
≤
4
extreme 2/(x+5)
extreme
2
x
+
5
extreme f(x)=-3x^3-63/2 x^2-90x+1
extreme
f
(
x
)
=
−
3
x
3
−
6
3
2
x
2
−
9
0
x
+
1
extreme f(x)=(x+4)/(x^2-3x-28)
extreme
f
(
x
)
=
x
+
4
x
2
−
3
x
−
2
8
extreme f(x)=2+9x+3x^2-x^3
extreme
f
(
x
)
=
2
+
9
x
+
3
x
2
−
x
3
extreme f(x)=cos(x)-2x
extreme
f
(
x
)
=
cos
(
x
)
−
2
x
extreme f(x)=(x-5)(x-3)(x+1)^2
extreme
f
(
x
)
=
(
x
−
5
)
(
x
−
3
)
(
x
+
1
)
2
extreme y=x^3-3x^2-9x+1
extreme
y
=
x
3
−
3
x
2
−
9
x
+
1
extreme f(x,y)=3x^2+y^2
extreme
f
(
x
,
y
)
=
3
x
2
+
y
2
extreme f(x)=-x^2-2x+1
extreme
f
(
x
)
=
−
x
2
−
2
x
+
1
extreme 3x^2+y^2-xy-11x
extreme
3
x
2
+
y
2
−
xy
−
1
1
x
extreme x^2-8x
extreme
x
2
−
8
x
extreme f(x)=x^3-6x^2+3
extreme
f
(
x
)
=
x
3
−
6
x
2
+
3
extreme f(x)=sqrt(x^2+9)
extreme
f
(
x
)
=
√
x
2
+
9
extreme 4/(x+6)
extreme
4
x
+
6
extreme f(x,y)=113x+15y-x^2-2y^2+3xy
extreme
f
(
x
,
y
)
=
1
1
3
x
+
1
5
y
−
x
2
−
2
y
2
+
3
xy
extreme (csc(x))/(1+csc(x))
extreme
csc
(
x
)
1
+
csc
(
x
)
extreme f(x)=x^{8/3},-8<= x<= 1
extreme
f
(
x
)
=
x
8
3
,
−
8
≤
x
≤
1
extreme f(x)=cos^2(x),0<= x<= pi
extreme
f
(
x
)
=
cos
2
(
x
)
,
0
≤
x
≤
π
extreme f(x)=x^3+2x^2-7x
extreme
f
(
x
)
=
x
3
+
2
x
2
−
7
x
extreme f(x,y)=xe^{-3x^2-3y^2}
extreme
f
(
x
,
y
)
=
xe
−
3
x
2
−
3
y
2
extreme f(x,y)=2x^2-8x+y^2-8y+2
extreme
f
(
x
,
y
)
=
2
x
2
−
8
x
+
y
2
−
8
y
+
2
extreme 1/(x-2)
extreme
1
x
−
2
extreme f(x,y)=x^2+y^2-6y+9
extreme
f
(
x
,
y
)
=
x
2
+
y
2
−
6
y
+
9
extreme f(x)=x^2,-1<= x<= 0
extreme
f
(
x
)
=
x
2
,
−
1
≤
x
≤
0
extreme f(x)=x^4-4x^3+16x+4
extreme
f
(
x
)
=
x
4
−
4
x
3
+
1
6
x
+
4
1
..
780
781
782
783
784
..
839
