revenue is found with he equation r=pq where p is the price charged and q is the quantity sold. If the price function is changing at a rate of 10 cents per day and the quantity sold is changing at -2 items per day. How is the revenue per day changing if the price is currently at $5 and the quantity sold is 100 items?
Denote the number of days passed as n, n>=0. Then p=p(n)=5+0.1n and q=q(n)=100-2n. Thetefore r=r(n)=(5+0.1n)*(100-2n)=500+10n-10n-0.2n^2=500-0.2n^2.
This function is relatively simple. Its graph is a parabola branches down with the vertex (maximum) at n=0 (r(0)=500$). It has a root at sqrt(500/0.2)=50 (days). I.e. revenue descends and after 50th day becames negative.