A more general form of the cobb douglas production function

Question

A more general form of the Cobb Douglas production function is q=f(L,K) =AL^aK^b, Where A, a, b > 0 are constants.

a) Use calculus to solve for the marginal product of labor (MPL).

b) Use calculus to solve for the marginal product of capital (MPK).

c) Using what you found in (a) and (b), what is the MRTS_L,K ?

d) In one sentence, interpret what the what is the MRTS_L,K tells you if A = 20, a= b = .5; and L=10; K=20

e) Suppose that A = 20; a = b= .5. Derive an equation for the isoquant q = 100 and graph it with labor on the x-axis and capital on the y-axis. Including at least two ordered pairs on your graph.