A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.

^dy/_dx = 9x^2 + 2ax + b

x = 2, ^dy/_dx = 9(2)^2 + 2a(2) + b = 36 + 4a + b

x = 1, ^dy/_dx = 9(1)^2 + 2a(1) + b = 9 + 2a + b

36 + 4a + b = 2(9 + 2a + b)

b = 18

x = -1, ^dy/_dx = 0 = 9(-1)^2 + 2a(-1) + 18

9 - 2a + 18 = 0

a = 13.5