Nama : Ratu Anna Soraya
NPM : 36112049
Kelas : 1DB08
MATDAS 2B
TUGAS KE 4
1. Tentukan nilai maksimum dan minimum f(x) = 3x5 –
5x3 – 30x
b) DF = { x | - 2 ≤ x
≤ 2
}
c) DF = { x | 2 ≤ x ≤ 4 }
JAWAB
f(x) = 3x5 – 5x3 – 30x
fI (x) =
15x4 – 15x2 – 30
y = x4 – x2 – 2 = 0
x4 – x2 – 2
( x2 + 1) (x2 – 2)
x2 + 1 = 0 x2
– 2 = 0
x2 = -1 x2 = 2
x = 
x
= 
x
=
b) f(x) = 3x5 – 5x3
– 30x
f ( - 
) = 3 ( - )5 – 5 ( - )3 – 30 ( - ) = 28
) = 3 ( - )5 – 5 ( - )3 – 30 ( - ) = 28
f(
= 3 ( )5 – 5 ( )3 – 30 ( ) = - 28
= 3 ( )5 – 5 ( )3 – 30 ( ) = - 28
f ( - 2 ) = 3 ( - 2
)5 – 5 ( - 2 )3 – 30 ( - 2
) = 4
f ( 2 )
= 3 ( 2 )5 – 5 ( 2
)3 – 30 ( 2 ) = - 4
Ø
Max = f ( - 
Ø
Min = f (2)
c) ) f(x) = 3x5 – 5x3
– 30x
f ( - ) = 3 ( - )5 – 5 ( - )3 – 30 ( - ) = 28
) = 3 ( - )5 – 5 ( - )3 – 30 ( - ) = 28
f( = 3 ( )5 – 5 ( )3 – 30 ( ) = - 28
= 3 ( )5 – 5 ( )3 – 30 ( ) = - 28
f ( 2 )
= 3 ( 2 )5 – 5 ( 2
)3 – 30 ( 2 ) = - 4
f ( 4 )
= 3 ( 4 )5 – 5 ( 4
)3 – 30 ( 4 ) = 2632
Ø
Max = f (4)
Ø
Min = f (2)
2. Tentukan nilai maksimum hasil kali dua
buah bilangan jika jumlah kedua bilangan tersebut sama dengan 20
Bila bilangan pertama = x
Maka = x ( 20 – x )
= 20x - x2
JAWAB
20 – 2x = 0 20
( 0 ) – ( 0 ) 2
2 ( 10 – x ) = 0 0
– 0 = 0
2 = 0 10 – x = 0
10 = x 20 ( 10 ) –
( 10 ) 2
X = 0 dan 10 200
– 100 = 100
Max = 10
Min = 0
TUGAS KE 5
1)
F ( X ) = 2X2 – X6 – 3X
FI ( X ) = 4X – 6X5 –
3
FII ( X ) = 4 – 30X4
2)
F ( X ) = X3 + 4X2 + 1
FI ( X ) = 3X2 + 8X
FII ( X ) = 6X + 8
3)
F ( X ) = 
F ( X ) = 4 ( 1 – 2X)-1/2
FI
( X ) = ( 2 ) 1/2
FII ( X ) = 
4)
F ( X ) = ( 3X2 – 1 ) 5
FI ( X ) = 5 ( 3X2 –
1 ) 4 . 6X
=30X ( 3X2 –
1 ) 4
FII
( X ) = 30X . 4 ( 3X2 – 1 ) 3 . 6X
= 720X ( 3X2 – 1 ) 3
Atau
F ( X ) = ( 3X2 – 1 ) 5
FI ( X ) = 
( 6X )4 . 6
( 6X )4 . 6
= 
( 6X )4
( 6X )4
FII ( X ) = . 
( 6 )3
. ( 6 )3
=
(6 )3
(6 )3
= 4 . 216
= 864
5)
F ( X ) = 
FI ( X ) = 
FII ( X ) = 
= 1
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