And Solve derivative for yln7x5x yIn x8 y t6 et My Notes o A

My Notes o Ask T. O-2 points A firm that produces Items has monthly average costs, in dollars per It given by the following function where qis the number of Items produced per month. AC(q) 39,000 100 q The firm can sell Items in a competitive market for $2000 per Item If production is limited to soo Items per month, find the number of items that gives maximum profit, find the maximum profit. Items maximum profit o -13 points of production and sale is You sell Things. The weekly demand function q Things is p 800 g dollars per Thing, and the average cost for AC(q) 300 2a dollars per Thing. (a) Find the quantity that will maximize profit. (b) Find the selling price at this optimal quantity. (c) What is the maximum profit?

Solution

Given y=ln(7x)/5x, then dy/dx=(5x*(1/x)-ln(x)*5)/(5*x)²=(5-ln(x)*5)/(5*x)²=(1-ln(x))/(5*x²)

given y=(ln x)⁸ =8(ln x), then dy/dx=8*(1/x)

Given y=t⁶*e^t ,then dy/dx=6t⁵ *e^t +t⁶*e^t