ECO- 5.2 Optimization and Hessians

(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)