Question

The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f(p).

What is the meaning of the derivative f '(8)?
1-the amount of coffee needed to be sold to charge $8 per pound
2-the rate of change of the price per pound with respect to the quantity of coffee sold
3-none of these are correct
4-the rate of change of the quantity of coffee sold with respect to the price per pound when the price is $8 per pound

Answer 1

5-the rate of change of the price per pound with respect to the quantity of coffee sold when the price is $8 per pound

Answer 2

would it be option 4?

Answer 3

p is our independent variable.
That's what we're differentiating with respect to, `with respect to price`.

\[\Large\rm f(p)=Q\]\[\Large\rm f'(p)=\frac{dQ}{dp}\]
Rate of change of quantity, with respect to price.

Yes option 4, that looks correct! :)

Answer 4

thanks!