1.    (1) A demand function is given by P = 24 – 6 ln Q.

(a)  Write down the equation for TR. Determine the value of Q at which TR is maximized
(b) 
Write down the equation for MR. Show, by differentiation, that MR decreases but never reaches zero; that MR is concave up
(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 345., number 1) soal differentian and application soal jawab differential and application number 1

2. A consumption finction is given by the equation
(a)
Write down the equation for the MPC. Hence describe how consumption changes as income increases
(b) 
Use differentiation to show the consumption has no maximum value
(c) 
Plot the consumption function. How would you describe the curvature of the consumption function ? Use the second derivative to confirm your answer
(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 346., number 2) soal jawab differential and application number 2

3. A utility function is given by the equation , where x is the number of glasess of wine consumed
(a) 
Show that this utility function ha s a maximum value and calculate the maximum utility
(b) 
Describe how marginal utility changes for glasses of wine consumed after the maximum utility reached. Do yo consider this reasonable ? give an explanation
(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 346., number 3) soal jawab differential and application number 3

4.   A firm’s average revenue function is AR =
(a) 
Determine the equations for TR and MR
(b) 
Find the value of Q fior which TR is maximum. Calculate the price and TR when TR is maximized
(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 346., number 4) soal jawab differential and application number 4

5.  The enjoyment derived from watching a particular film is given by the equation , where t is the viewing time in minutes
(a) 
Graph the utility function for the first two hours of viewing time. Hence describe how enjoyment changes as the film progress
(b) 
Determine the equation for marginal utility and plot its graph
(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 346., number 5) soal jawab differential and application number 5

6.    Given
(
a)  Find the minimum AC and graph the AC function for Q=0 to Q = 25
(b) 
Write down the equation of TC
(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 346., number 6) soal jawab differential and application number 6

 7.     (a) Differentiate the following,
(i)  
            (ii)
(b) 
The demand function for safari holidays is given by the equation , where P is the price of the holiday and Q is the number of travelers
(i)  
Write down the equation for total revenue and marginal revenue
(ii)
Calculate the number of travelers on a safari (Q) for which the total revenue is maximized. Calculate the maximum revenue
(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 346., number7) soal jawab differential and application number 7

 8.   (a) Dffrentiate the following (i) , (ii)
(b )The demand function for hand- painted T-shirt is given by the equation
 while the average cost function is  (i) Write down the equations for total revenue and marginal revenue (ii) Calculate the quantity which must sold to maximize total revenue. Calculate the maximum revenue (iii) Confirm your answer in (ii) by graphing the total revenue function
© (i) Write down the equation of total cost and marginal cost (ii) write down the equation for profit (iii) Calculate the maximum profit. How many T shirt must be produced and sold to maximize profit?

(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 346., number 8) soal jawab differential and application number 8

 9.   9. (a) Differentiate the following (i)  (ii) . Hence determine the maximum and minimum points using the slope test
(b) A firm has average cost function
, (i) Calculate the value of Q for which the average costs are minimum. Hence state the range of values for which average costs are decreasing (ii) Write down the equation for total cost. Hence calculate the value of Q for which total costs are minimum
(c) 
If a government subsidy of 3 per unit produced is given, write down the equation for total cost. Hence calculate the value of Q for which total costs are minimum
(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 347., number 9)soal jawab differential and application number 9

10.See question 2, progress exercise 4.8
(a) 
Diffrentiate the following
(b) 
The sales og magazine are expected to grow according to the equation in (a) where t is ini weeks. Show by differentiation that sales never reach an exact maximum value. What is the limiting sales value approached?
(Teresa Bradley., Essential Mathematics for Economics and Business., Wiley., Fourth Edition., page 347., number 10) soal jawab differential and application number 10