Question: business mathematics for mba by richard p waterman 1st edition...
*****Business mathematics for MBA by Richard P. Waterman 1st Edition*****
*****Must show all works and formulas you use*****
Module 6 questions Module 6. Q1. Find the derivative with respect to x of the following (a) f (x) = 6x 2 + 5x (b) y = 5 x + 4x
Module 6. Q2. Find the derivative with respect to x of the following y = 7 + 4 x 2 x 2 (#WIIGD6LC)
MODULE 11. PRACTICE QUESTIONS 254 Module 6. Q3. Find the derivative with respect to x of the following (a) f (x) = (x + 1 x ) 2 (b) y = p x + 1 p x (c) y = x 2n nx 2 + 5n
Module 6. Q4. Identify the points (for x greater than zero) with zero slope and the value of the function there on the curves (a) f (x) = x(x 2 12) (b) y = x + 1 x
Module 6. Q5. Find the derivative of the following (a) f (x) = e x 2 (b) y = e qx (c) y = e ln x
Module 6. Q6. Find the derivative of the following using the rule for products (a) f (x) = x 3 x 3 (b) y = (x 2 5)(x 2 + 5) (c) f (x) = e x x
Module 6. Q7. Find the derivative of the following using the chain rule (a) y = f (t) = p 1 t 2 (b) y = f (t) = (t 2 3t + 5) 2 (c) y = f (t) = e t 2 (d) y = f (t) = e t 1+e t
Module 6. Q8. Suppose the demand function for a certain product is q = 200 4p, where p is the price per pound and q is the quantity demanded(in millions). (a) What quantity can be sold at $30 per pound? (b) Determine the elasticity of demand, e(p), where e(p) = dq dp p q . (c) Determine and interpret the elasticity of demand at e(30).
Module 6. Q9. The total cost of producing x units of a certain commodity is given by C (x) = 800 + 40x. (a) Find the average cost function A(x), which is dened as A(x) = C(x) x . (b) Find the derivative of the average cost function A 0 (x) (c) Interpret the sign of the result from part (b).
Module 6. Q10. The costs of a particular manufacturing process can be classified as one of two types: the cost of labor and cost of capital. A useful production function used in economics is known as the Cobb-Douglas production function and in this instance would be written as f (x; y) = Cx 1 y 2 , where x is the number of units of labor, y the number of units of capital 1; 2 and C are constants. Suppose that during a certain period of time the number of units of goods produced when using x units of labor and y units of capital is f (x; y) = 80x 3=4 y 1=4 . (a) How many units of goods will be produced by using 81 units of labor and 16 units of capital? (b) Suppose the number of units of capital, y, is xed at 16, nd the elasticity, df (x;16) dx x f (x;16) and interpret the result. (c) Suppose the number of units of labor, x, is xed at 81, nd the elasticity df (81;y) dy y f (81;y) and interpret the result. (d) If both inputs doubled what would happen to the output?