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# (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)

(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)

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