5. Üstel-Logaritmik Fonksiyonlar

93 Pages·2005·0.47 MB·Turkish

ÜSTEL VE
ÜSTEL VE
LOGARİTMİK
LOGARİTMİK
FONKSİYONLAR
FONKSİYONLAR
22
ŞŞeekkiill 55..11aa ÜÜsstteell FFoonnkkssiiyyoonnllaarr
y
10
( ) t
y = f t = b , b > 1
8
6
4
2
•
t
-3 -2 -1 1 2 3
33
ŞŞeekkiill 55..11bb ÜÜsstteell FFoonnkkssiiyyoonnllaarr
y
y = f (t ) = 22t
50
40
30
20 y = f (t ) = 2t
10
t
-2 -1 1 2 3 4
44
ŞŞeekkiill 55..11cc ÜÜsstteell FFoonnkkssiiyyoonnllaarr
y
( )
8 y = f (t ) = 2 2t
6
4
y = f (t ) = 2t
2
t
-2 -1 1 2
55
( ) t
y = f t = b , b > 1
( ) t
y = f t = b > 0 , − ∞ < t < ∞
d
( ) ( )
ln y = ln b t → ln y = ln b
dt
( )
dy y
= ln b
dt
dy
= f ′ ( t ) = ( ln b) bt > 0 , − ∞ < t < ∞
dt
66
2
d y
2
= f ′′ ( t ) = (ln b) bt > 0 , − ∞ < t < ∞
2
dt
( ) ( )
t t
lim b = ∞ , lim b = 0
t→∞ t→−∞
77
( ) ct
y = f t = ab , b > 1
f ′ ( t ) = ac ( ln b) bct
( )
a > 0 , c > 0 → f ′ t > 0
( )
a > 0 , c < 0 → f ′ t < 0
( )
a < 0 , c > 0 → f ′ t < 0
( )
a < 0 , c < 0 → f ′ t > 0
88
2
f ′′ ( t ) = ac2 ( ln b) bct
( )
a > 0 → f ′′ t > 0
( )
a < 0 → f ′′ t < 0
99
ŞŞeekkiill 55..22aa ÜÜsstteell FFoonnkkssiiyyoonnllaarr
y y
0 t 0 t
y = f ( t ) = abct y = f ( t ) = abct
a > 0 , c > 0 a > 0 , c < 0
1100
ŞŞeekkiill 55..22bb ÜÜsstteell FFoonnkkssiiyyoonnllaarr
y y
0 0
t t
y = f ( t ) = abct y = f ( t ) = abct
a < 0 , c < 0 a < 0 , c > 0