1. No category

notes
"! "
!
!
#
f (x)
x
log 2 x
2
log 4 x 2
2
ab
c
log a c
b
a 0
a 1
c 0
x
0
log 2 x
2
log 2 x
2
log 2 x
2
log 2 x
log 4 x 2
log 2 x 2
log 2 4
2 log 2 x
2
2
log2 x
log 2 x log 2 x 1
log 2 x
t
2
t
0
0
0
0
0
t
0
t2 0
log 2 x 1
x
t1 1
log 2 x 1
20
x
x 1
x
(1,0)
x
21
2
(2,0)
2
y
f (x)
f ( 2)
2
log 2 x
log 2 2
f ( 2)
2
log 2 x
log 2 2
0.5
f ( 2)
2
0.5
0.25 0.5
f ( 2)
0.25
( 2, 0.25)
f (x)
log 2 x
2
log 4 x 2
2 log 2 x log 2 x ' (log 4 x 2 ) '
1
f '(x) 2 log 2 x
(log 4 x 2 ) '
x ln 2
1
f '(x) 2 log 2 x
(log 2 x) '
x ln 2
1
1
f '(x) 2 log 2 x
x ln 2 x ln 2
2
1
f '(x)
log 2 x
x ln 2
x ln 2
1
f '(x)
(2 log 2 x 1)
x ln 2
f '(x)
f '(x)
f '( 2)
1
(2 log 2 x 1)
x ln 2
1
(2 log 2 2 1)
2 ln 2
1
1
(2
1)
0.98
2
0
y1
0.25
x1
2
m 0
(y
y1 )
y ( 0.25)
m(x
x1 )
0(x
2)
y 0.25 0
y
0.25
$
f (x) ln x
2
5x 6
y
IV III II I
x2
x
x
3
f (1.99) ln 0.0101
5x 6 0
2
4.6
f (1.9999) ln 0.00010001
9.21
f (1.99999999) ln 0.00000001
18.42
y!
f (x) ln x 2
f '(x)
1
(x
2
5x 6) ln e
x2
x
2
x
3
5x 6
5x 6 '
1
x
2
2x 5
5x 6
2x 5
2
5x 6
2x 5
x2
5x 6
x
f '(x)
2
1
f '(4)
x<2
x=1
!
y'
x
0
5x 6
2x 5 0
2x 5
! x 2.5
2 1 5
f '(1)
x
2x 5
2
4
3
2
5 1 6
2 4 5
2
3
1.5
2
5 4 6
x>3
x=4
"
x=3
x=2
1.5
x<2
x>3
%!
II
$!
x>3!
x
#
x<2!
#
II! I
II
x
f (x) ln x 2
5x 6
0
ln x 2
5x 6
0
x2
6
e0
5x
1 x
2
5x 6
0
2
5x 5
3.62
x
x1
x 2 1.38
1.38
2
3
3.62
1.38 x
3 x
2
3.62