(a) Find $\displaystyle \frac{dy}{dx}$ expressed as a function of t for the given the parametric equations: $$\begin{array}{r@{\,}c@{\,}l} x & = & \cos^{3}(t) \cr y & = & 6 \sin^2(t) \end{array}$$ $\displaystyle \frac{dy}{dx} =$ .
(b) Find $\displaystyle \frac{d^2 y}{dx^2}$ expressed as a function of t.
$\displaystyle \frac{d^2y}{dx^2} =$ .
(c) Except for at the points where $\displaystyle \frac{dy}{dx}$ is undefined, is the curve concave up or concave down? (Enter 'up' or 'down').
Concave .