Suppose the production function is y=f(K,L)=K³L, where K is capital input and L is labor input, K>0, L>0.

1. What are the marginal products of capital and labor repectively?
2. Calculate the technical rate of substitution(assume K is on the horizontal axis).
3. Dose this production function show diminishing technical rate of substitution(in absolute value) when K increases? Please give a brief proof.
4. Prove that this production function features increasing returns to scale for all t>1, where t is a constant.Please give a brief proof.