Answer question 1 a)-g)

Question 1 (10 points) Find the following derivatives and limits a) (1 point) lim - In (x+1) b) (1 point) lim In (x+1) c) (1 point) lim x-o In(x+1) -x d) (1 point) Find - x (y) at point y=0, if x (y) is an inverse function of a function y (x), y(0) = 1, y(1) = 0, y'(0) = 2, and y' (1) = 5 e) (2 points) =-logx(x2 + 1) f) (2 points) - In((x + 1)*+1) g) (2 points) Find = at point (x,y)=(2,2) ify(x) is defined by equation In(y) + y + 2 = In(x) + 2x Question 2 (7 points): Consider a function f (x) = 3x* - 28x3 + 66x2 - 60x + 15 a) (2 points) One of the stationary points of f (x) (i.e., a point where f' (x) = 0 ) is x = 1. Find all other stationary points b) (2 points) Using second derivative test, can you tell which of stationary points are local maxima and which are local minima c) (1 point) For x=1, use the first derivative test to determine if it is local maximum, minimum, or neither d) (1 point) Find the points of inflection for f (x) e) (1 point) For which x function f(x) is concave down Question 3 (3 points): The firm's production function is given by Q (x) = 200x - 200vx. where x is the number of people the firm employs. Currently the firm employs 100 people a) ( 1 point) Find the Marginal Product of Labor (MPL), i.e., Q'(x) at x=100 b) (2 points) The firm is a monopolist and faces a demand function P(Q) = 400 - 20In (Q + 1). Find the Marginal Revenue of Labor (MRL), i.e., - ( Note: MRL can dx be used the determine if the firm needs to hire more people (if MRL- wage) or fire some (if MRL