points (1,4) and (2,12) lie on a curve whose gradient is giiven by dy/dx=6x2-6x+k a)find the value of k b)the equation of the curve

Answer 1

y = 2x³ - 3x² + kx + C

Since (1,4) is on the curve, 2 - 3 + k + C = 4

Since (2,12) is on the curve, 16 - 12 + 2k + C = 12

So, we have the system of equations:

k + C = 5

2k + C = 8

Solve for k and C.