The line (y = mx – 3) is a tangent to the curve (y = 1 – 3x + 2x^{3}) at (1, 0). Find the value of the constant m.
-
A.
-4 -
B.
-1 -
C.
3 -
D.
4
Explanation
(y = 1 – 3x + 2x^{3})
(frac{mathrm d y}{mathrm d x} = -3 + 6x^{2})
At (1, 0), (frac{mathrm d y}{mathrm d x} = -3 + 6(1^{2}) = -3 + 6 = 3)
(y = mx – 3 implies frac{mathrm d y}{mathrm d x} = m = 3) (Tangent with equal gradient)