# Question: business mathematics for mba by richard p waterman 1st edition...

###### Question details

*******Business
mathematics for MBA by Richard P. Waterman 1 ^{st}
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?