A curve is defined by the parametric equations x=t^2/2 +1, y=4/t -1. Find the gradient of the curve when t =2.

Firstly we would differentiate each equation with respect to t to find dx/dt and dy/dt- which gives us dx/dt=t and dy/dt=-4t^-2. Once you have found these you must divide dy/dt by dx/dt (or dy/dt x dt/dx) which is dy/dx= -4t^-3. Then you can sub t=2 into your dy/dx to find the gradient of the curve at that point to find the answer is -1/2.