bendjol
1. y = x²-4x+2 y' = 2x-4; y' = 0 0 = 2x-4 2x = 4 x = 2
y = x²-4x+2 = (2)²-4(2)+2 = -2 koordinat titik balik : (2,-2)
2. 4x = -y²+3y+5 4x' = -2y+3 2y = 3 y = 3/2
4x = -y²+3y+5 4x = -(3/2)²+3.(3/2)+5 x = 29/16 koordinat titik balik : (29/16 , 3/2)
3. y = 3x²-2x+15 y' = 6x-2; y' = 0 0 = 6x-2 6x = 2 x = 1/3
y = 3x²-2x+15 = (1/3)²-2(1/3)+15 = 130/9 koordinat titik balik : (1/3 , 130/9)
4. y = x³-4x²-3x+8 y' = 3x²-8x-3; y' = 0 0 = 3x²-8x-3 0 =(x-3)(3x+1) x = 3 atau x = -1/3
uji max n min menggunakan turunan kedua: y'' = 6x-8
saat x = 3, maka y = 6.(3) - 8 = 10 ; y > 0 (minimum) minimum saat x = 3 y = x³-4x²-3x+8 = 3³-4(3)²-3(3)+8 = -10 koordinat titik balik minimum : (3, -10)
saat x = -1/3, maka y = 6(-1/3)-8 = -2-8 = -10 ; y < 0 (maksimum) maksimum saat x = -1/3 y = x³-4x²-3x+8 = (-1/3)³-4(-1/3)²-3(-1/3)+8 = 8+(14/27) = 230/27 koordinat titik balik minimum : (-1/3 , 230/27)
y' = 2x-4; y' = 0
0 = 2x-4
2x = 4
x = 2
y = x²-4x+2
= (2)²-4(2)+2
= -2
koordinat titik balik : (2,-2)
2. 4x = -y²+3y+5
4x' = -2y+3
2y = 3
y = 3/2
4x = -y²+3y+5
4x = -(3/2)²+3.(3/2)+5
x = 29/16
koordinat titik balik : (29/16 , 3/2)
3. y = 3x²-2x+15
y' = 6x-2; y' = 0
0 = 6x-2
6x = 2
x = 1/3
y = 3x²-2x+15
= (1/3)²-2(1/3)+15
= 130/9
koordinat titik balik : (1/3 , 130/9)
4. y = x³-4x²-3x+8
y' = 3x²-8x-3; y' = 0
0 = 3x²-8x-3
0 =(x-3)(3x+1)
x = 3 atau x = -1/3
uji max n min menggunakan turunan kedua:
y'' = 6x-8
saat x = 3, maka y = 6.(3) - 8
= 10 ; y > 0 (minimum)
minimum saat x = 3
y = x³-4x²-3x+8
= 3³-4(3)²-3(3)+8
= -10
koordinat titik balik minimum : (3, -10)
saat x = -1/3, maka y = 6(-1/3)-8
= -2-8
= -10 ; y < 0 (maksimum)
maksimum saat x = -1/3
y = x³-4x²-3x+8
= (-1/3)³-4(-1/3)²-3(-1/3)+8
= 8+(14/27)
= 230/27
koordinat titik balik minimum : (-1/3 , 230/27)