Take the first second and cross derivative of fkn explain

Question

Let the F(K,N) = K↵N1−↵ with ↵ ∈ (0,1):

(a) Take the first, second, and cross derivative of F(K,N). Explain what the sign of each one means.

(b) Divide the function by N and show that the function can be written as F(K,N) = (KN)↵.

(c) Letting k = KN, express F(K,N) as a function of just k and let that be f(k).

(d) Take the first and second derivative of f(k). Explain what the sign of each o