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 is C

\(y = 4x^{3} + kx^{2} - 6x + 4\)

\(\frac{\mathrm d y}{\mathrm d x} = 12x^{2} + 2kx - 6\)

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)