October 28, 2014
4-5
Derivatives of
Logarithmic Functions
Find the derivative
Find the derivative
Find the derivative
Find the derivative
October 28, 2014
Find the derivative
Find the derivative
Assume that the total revenue received from the sale of x items is given
by, R(x) = 35 ln (3x + 4), while the total cost to produce x items is
C(x) = x/4. Find the number of items that should be manufactured so
that the profit R(x) - C(x) is a maximum. (Hint: set the derivative of the
profit function equal to 0.)
Find the derivative
Assume that the total revenue received from the sale of x items is given
by, R(x) = 35 ln (3x + 4), while the total cost to produce x items is
C(x) = x/4. Find the number of items that should be manufactured so
that the profit R(x) - C(x) is a maximum. (Hint: set the derivative of the
profit function equal to 0.)
The cost function for q units of a certain item is C(q) = 107q + 104. The
revenue function for the same item is:
a) Find the marginal cost.
b) Find the profit function.
c) Find the profit function from one more unit sold when 8 units are sold.
October 28, 2014
The Richter scale provides a measure of the magnitude of an
earthquake. The following formula shows a relationship between the
amount of energy released and the Richter number.
a) What value of E gives a Richter number M = 8.3? (use scientific
notation)
The Richter scale provides a measure of the magnitude of an
earthquake. The following formula shows a relationship between the
amount of energy released and the Richter number.
c) Find the rate of change of the Richter number M with respect to
energy when E = 75,000 kWh.
b) If a particular household uses 240 kWh per month, how many months
would the energy released by an earthquake of this magnitude power 10
million households?
YOU CAN ALSO USE YOUR CALCULATOR TO FIND THE DERIVATIVE FOR PART C