Assuming That the Equations Define X and Y Implicitly as Differentiable

Multiple Choice

Assuming that the equations define x and y implicitly as differentiable functions x = f(t) , y = g(t) , find the slope of the curve x = f(t) , y = g(t) at the given value of t.
- $$2 x + 4 x ^ { 3 / 2 } = t ^ { 3 } + t , y ( t + 1 ) - 4 t \sqrt { y } = 4 , t = 0$$

A) -8
B) 2
C) 8
D) 4