Given that (frac{mathrm d y}{mathrm d x} = 3x^{2} – 4) and y = 6 when x = 3, find the equation for y.
-
A.
(x^{3} – 4x – 9) -
B.
(x^{3} – 4x + 9) -
C.
(x^{3} + 4x – 9) -
D.
(x^{3} + 4x + 9)
Correct Answer: Option A
Explanation
(frac{mathrm d y}{mathrm d x} = 3x^{2} – 4)
(y = int (3x^{2} – 4) mathrm {d} x = x^{3} – 4x + c)
y = 6 when x = 3
(6 = 3^{3} – 4(3) + c implies 6 = 27 – 12 + c)
(c = 6 – 15 = -9)
(y = x^{3} – 4x – 9)