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
AR
Answered by Alistair R. • Further Mathematics tutor
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