(Problem is easier to understand in the attachment)

5.2 Optimization and Hessians (10 Points)

Consider the production function

Q = 4K ^ (3/4) * L ^ (1/4)

a. Find the gradient of Q

b. Find the Hessian of Q

c. Denote the initial K = 10,000 and L = 625. Consider an increase of K by ?K and similarly an increase of L by ?L. Find the Taylor approximation for this function. f(x + ?x) = f(x) + ?x^(T) * ?f(x) + (1/2)?x^(T) * H(x)?x + o(k ?x k2)

(problem is easier to understand in the attachment)