ok, I am completely at a loss - I don't even know where to begin.

for (a): I should find the slope of T - but I have no idea how - could I make a triangle and solve for the hyp? so would it be like $\displaystyle f'(a) = \sqrt{PQ^2 + QT^2}$

and then I am at a complete loss, partially because the given diagram is so confusing ... any help would be greatly welcomed