Finding maxima and minima Question 1. Let f(x) = + Find all relative maxima and minima of this function. Find the absolute maximum and minimum on the interval [3, 5]. Integration Question 2. and y(0) = 0. Find y(1). dy dr - 4x(x + 4)- Question 3a. ( + )dx Question 3b. de Caution, the funtion f(x) x = 0. In such a case how is the integral defined? Question 3c. e+2 dz Question 3d. In(r)dr Multivariable = is not defined at Question 4a. Let f(x,y) = x + xy + y + 4x + 5y Find the relative maxima and minima of this function. Question 4b. Let f(x, y) 2-3y2 What is the critical point of this function? What type of a critical point is it and why? Question 4c. Assume that the production capacity (Y), which depends on the amount of labor force (L) and the amount of capital (K), of a company is given by Y(K, L) = 2K0.25L0.75, Find the marginal product of labor if the company hires 16 workers and rents a capital of $ 810000. Remember marginal product of labor is ? Lagrange Multipliers Question 5. On the constraint function g(x, y) = x + 3y29 with the constraint g(x, y) = 0 find the maximum of the function f(x, y) = 2x + 3y Question 6. On the constraint function g(x, y, z) = 2 - y - + 1 with the constraint g(x, y, z)= 0 find the maximum or minimum of the function f(x, y, z) = 2x+3y. Can you determine whether this is a maximum or minimum using some reasoning?