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.
- $$x ( t + 1 ) - 4 t \sqrt { x } = 36,2 y + 4 y ^ { 3 / 2 } = t ^ { 3 } + t , t = 0$$

A) $- 24$
B) $- 12$
C) $- \frac { 1 } { 24 }$
D) $- \frac { 1 } { 12 }$