Use the Leibniz’s way to find derivative of the function

Problem 1.

Given,

a)    Use the Leibniz’s way to find derivative of the function.

b)    Find the value of the derivative at .

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Problem 2

Assume that a demand equation is given by . Find the marginal Revue for the given production levels (values of ). (Hint: Use the demand equation to express  as a function of , and replace  in the revenue function)

a)    1000 units

b)    2500 units

c)    3000 units

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Problem 3

The revenue and cost functions for producing and selling quantity  for a certain production facility are given below.

a)    Determine the profit function .

b)    Use Excel to graph the functions  and  for the interval . Copy and paste the graph below. (Hint: Use Scatter plot with smooth lines and markers.)

c)    Compute the break-even quantities.

d)    Determine the marginal revenue .

e)    Determine the marginal cost

f)     At what quantity is the profit maximized?

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