QUESTION 1 (a)

(a) (i) A curve LaTeX: P is defined parametrically as LaTeX: x=\frac{t}{1+t},\:\:\:y=\frac{t^3}{\left(1+t\right)}.

Determine the gradient of the curve at the point LaTeX: \left(\frac{1}{2},\:\frac{1}{2}\right).
(ii) Hence, or otherwise, determine the LaTeX: x and LaTeX: y intercepts of the tangent that touches the curve at the point LaTeX: \left(\frac{1}{2},\:\frac{1}{2}\right).