tentukan persamaan kurva y=f(x) jika gardiennya m=dy/dx(x-1)3 dan melalui titik A(3,0)

jawab


m = dy/dx = (x -1)³
y= ∫dy/dx

y= ∫ (x -1)³ dx 
y = 1/4 (x - 1)⁴ + c 
melalaui (3,0), x = 3, y = 0
0 = 1/4 (3-1)⁴ + c
0 = 1/4(16) + c
0  = 4 + c
c = - 4

persamaan kurva = 1/4 (x-1)⁴ - 4