I've really only been able to do part a with iL(0+)=0 A, Vc(0+) = -10V (which I would like someone to explain the justification, I saw an example in the book with a similar situation and am assuming it is correct), Vr (0+)= -10 V.
What steps would I take to find the rates of change? Thanks.

 

You need to show your work in order for us to help you much.

You might consider how Vr(0+) can be -10V if Vc(0+) is -10V. If both of those are true, what would the voltage across the voltage source have to be? How does that compare with what it is given to be?