The quantity (in yards) of a certain fabric that is sold by a manufacturer at a price of p dollars per yard is Q = f(p).
1) What is the meaning of the derivative f ' (16)?
2) What are its units?
3) Is f ' (16) positive or negative? Explain.
f'(p) is the rate of change of quantity as price changes
Think of the units:
f is yards
p is dollars, so
df/dp = yards/dollar
no idea whether f'(16) is positive or negative. However, it is likely that as price goes up, demand goes down.