The tangent to the curve (y = 4x^{3} + kx^{2} – 6x + 4) at the point P(1, m) is parallel to the x- axis, where k and m are constants. Determine the coordinates of P.
-
A.
(1, 2) -
B.
(1, 1) -
C.
(1, -1) -
D.
(1, -2)
Correct Answer: Option C
Explanation
(y = 4x^{3} + kx^{2} – 6x + 4)
(frac{mathrm d y}{mathrm d x} = 12x^{2} + 2kx – 6)
At P(1, m)
(frac{mathrm d y}{mathrm d x} = 12 + 2k – 6 = 0) (parallel to the x- axis)
(6 + 2k = 0 implies k = -3)
(P(1, m) implies m = 4(1^{3}) – 3(1^{2}) – 6(1) + 4)
= -1
P = (1, -1)