DIFFERENTIATION

1. For the following function find the:

1. First-order derivative

2. Second-order derivative

3. Value of the second-order derivative when x=4

f (x) = 2x3 + 4x2 + x 3 a. dQ forthesupplyfunctionQ=2P2+P+1

b. dQ for the production function Q = 200L + 4 4 L dL

3. Differentiate

1. y = 10e4x 2x2 + 7

2. y = (x2 + 3x 5)3

3. y = x2(x + 5)3

4. y= x2 x+4

2. Find expressions for

dP

Homework 11

4. Find and classify the stationary point:

   y = x2 + x + 1

5. The relationship between the Price/Book (PB) and Long-term Debt/Capital (LTD) is shown

   below.

   PB = 3.56 0.113(LTD) + 0.002(LTD)2

What level of Long-term Debt/Capital will minimise the Price/Book ratio of firms?