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. Find the value of k.
-
A.
3 -
B.
2 -
C.
-3 -
D.
-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)