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The tangent to the curve y=4x3+kx26x+4 at...

The tangent to the curve y=4x3+kx26x+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=4x3+kx26x+4

dydx=12x2+2kx6

At P(1, m)

dydx=12+2k6=0 (parallel to the x- axis)

6+2k=0k=3

\(P(1, m) \implies m = 4(1^{3}) - 3(1^{2}) - 6(1) + 4)

= -1

P = (1, -1)