let f(x,y) = (3x^3)(y) - (4x^2) (sqrt(y)) and let γ(t) = <x(t),y(t)> be a curve in the Oxy plane such that at some point t0, we have γ(t0) = (-1,4) and γ'(t0) = (-2,-3). Find the tangent vector r'(t0) to the curve r(t) = <x(t),y(t), f(x(t), y(t))> at the point t0.
Answer options:
(A). <-2, -3, -92>
(B). <-1, 4, -92>
(C). <-2, -3, -16>
(D). <-1, -1, -16>
(E). <52, -4, -1>