Ava Richardson, the proprietor of the Ava's Elegance store, predicts that when a specific type of hand lotion is priced at p dollars per tube, she will sell a B(p) number of tubes per monthB(p)=p+3500 p5

each at a total cost ofC(p)=0.2p2+3p+200

a. Represent Ava's profit P(p) as a function of the price p per tube?

b. What is the rate of change in profit in relation to p when the price is set at $12 per tube? Is the profit trend ascending or descending at this price point?