# derivatives of log function application

• Feb 21st 2009, 01:37 PM
shannon1111
derivatives of log function application
suppose the demand function for q units for a certain item is

p=d(q)=100+(50/lnq),q>1

where q is in dollars

a) find the marginal revenue.
b)approximate the revenue from one more unit when 8 units are sold.
c)how might a manager use the information from part b?

As for this one, I figuared out that R'=50q^2+50/lnq+100

but I have no idea for part b and c
• Feb 21st 2009, 04:35 PM
HallsofIvy
Quote:

Originally Posted by shannon1111
suppose the demand function for q units for a certain item is

p=d(q)=100+(50/lnq),q>1

where q is in dollars

You have already said that q is "units for a certain item". Did you mean to say that p is in dollars?

Quote:

a) find the marginal revenue.
b)approximate the revenue from one more unit when 8 units are sold.
c)how might a manager use the information from part b?

As for this one, I figuared out that R'=50q^2+50/lnq+100

but I have no idea for part b and c
The "revenue from one more unit when 8 units are sold" is R(9)- R(8).
Because R'(8)= lim (R(8+h)- R(8))/h, we can approximate R'(8) by taking h= 1. R'(8) is approximately R(9)- R(8). What is R'(8)?