help--derivatives?

Question

Answer 1

11)

Step 1:

Intial rent of the truck is $20/day when 30 trucks are rented.

For every $1 increase in rent of the truck, the number of trucks rented decrease by one.

Let times the rent of the truck is increase then number of trucks rented decrese by .

And cost function is .

Step 2:

Find the profit function.

Profit = Revenue - Costs

Apply derivative on each side with respect to .

.

Step 3:

Find the extreme(maximum) value of profit function by solving .

Therefore, the rental charge that produces the maximum profit is when per day.

Solution:

The rental charge that produces the maximum profit is when per day.