garis singgung parabola y = x ^2- 2 x + 8 di titik berabsis 2, menyinggung kurva y = a ^ 3 + bx -4 titik yang berabsis 1. nilai a - b adalah.....

y = x²-2x+8
absis = 2
menyinggung -> y = ax³+bx-4
absis = 1

pgs persamaan 1
y = x²-2x+8
y = (2)²-2(2)+8 = 4-4+8
y = 8

y' = m
2x -2 = m
2(2) - 2 = m
m = 2

pgs -> y-y1 = m(x-x1)
y - 8 = 2(x-2)
y = 2x-4+8
y = 2x+4

pgs persamaan 2
y = ax³+bx-4
y = a(1)³+b(1)-4
y = a+b-4

y' = m
3ax² + b = m
3a(1)² + b = m
m = 3a + b

Pgs -> y-y1 = m(x-x1)
y-(a+b-4) = (3a+b)(x-1)
y = 3ax - 3a + bx - b + (a+b-4)
y = (3a+b)x + (-2a-4)

pgs persamaan 1 = pgs persamaan 2

2x+4 = (3a+b)x + (-2a-4)

4 = -2a-4
-2a = 8
a = -4

2 = 3a+b
2 = 3(-8) + b
b = 2 + 24 = 26

a - b = -4 - 26 = -30