1. Obtain all the possible differential of the following function 100x^6+x^5+x^4+x^3+x+10
2. Find the third derivative of 10x^3-3x^2-5x+6
3. Find the Marginal Revenue, Marginal Cost and Marginal Profit of the following

A. R=60Q-2Q^2-200

B. TC=3Q^2-12Q-100

4. A process for a company in Nairobi has a total cost function given by TC=20+4x and a revenue function given by TR=22+4x^2, where X is the level of activity (in hundreds), TC and TR are both in units of Sh. 1,000.

Required:

A. Derive an expression for the total profit

B. Calculate the level of activity that maximizes profit and the amount of profit in shillings at this level

C. What is the profit situation when 500 units are produced?

5. Suppose a total cost function is given by TC= 0.01Q^2+5Q+100,where TC is total cost ($) and Q is output (units). Find the output level that minimizes average total cost (ATC)

6. The demand equationof a firm's product is given by p=-5Q+3,000.

The firm's total cost equation is given by p=50Q+10,000.

All values are in Shs and quantities in units. Determine

A. The quantity that maximizes revenue

B. The quantity and price that maximizes profits

C. The maximum profit