Question

3. Let ?(?) be the revenue in dollars from selling ? units. If ?(200) = 540 and ?′(200) = 17..

a. Verbally interpret ?(200)

b. Estimate the revenue generated from the production of 201 units.

c. If the cost in dollars to produce ?? units is given by ?(?) = ?.??x , is it profitable to raise the production to

201 units? Explain in a sentence.

4. An online shopping website has determined that the number of items orders they receive is modeled by ?(?)= t^3 − 6t^2+170 , where ? is the number of hours after 12 pm. At what rate is the number of items orders changing with respect to time, at 8pm?

5. When the ticket price for a concert at the opera house was $50, the average attendance was 4000 people. When the ticket price was raised to $52, the average attendance was 3800 people. Let x be the number of attendees and ? be the price of each ticket.

a. Assuming the demand function is linear, find the demand function that yields the price, ?(?).

b. Find the revenue function, ?(?)

c. Find the number of tickets sold that maximize the revenue. Remember to verify the value you found is a

maximum by making a sign chart.

d. Find the price that maximizes the revenue.

e. Find the maximum revenue.

6. Consider the function ?= (2? − 3)^3(−4?^2+1)^2

a. Find the derivative of ?. Factor final answer as much as possible.

b. Find the equation of the tangent line to the curve at the point (1,25)

please help

please help with all parts of number 5 and 6b

Answer 1

comment it asap please