To find the expansion path for K given a production function with K and L as the only inputs, first find the O minimum points of the marginal products of K and L. Then substitute the marginal products from the production function and solve for K. O tangency between the isoquant and isocost functions. Then substitute the prices of labor and capital and solve for K. O tangency between the isoquant and isocost functions. Then substitute the marginal products from the production function and solve for K. tangency between the isoquant and isocost functions. Then substitute the optimal value of Land solve for K.