Differentiate the function. f'(x) = f(x) = (3x7 - 4)16 Differentiate the function. 3 h(x) = (x5 - 3x3 + 2)8 4 h'(x) = Differentiate the function. s(t) = 3t 4(3+4 + 3) 3 - s'(t) =

The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x)=64x-0.020x² 0≤x≤3200 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. ... (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. 23 (Round to one decimal place as needed.) (B) R'(x) =

Suppose that the dollar cost of producing q appliances is c(q) = 1500 + 80q - 0.1q?. (a) Find the average cost per appliance of producing the first 150 appliances. (b) Find the marginal cost when 150 appliances are produced. (a) The average cost per appliance of producing the first 150 appliances is S per appliance. (Round to the nearest cent as needed.)

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Find the maximum of the function f defined as f(x) = 4x - 2x2 - 110 A

A bagel shop sells 400 bagels a day at a price of $2 per bagel. Market research shows that a decrease of price of $0.1 would increase sales by 10 bagels per day. Furthermore, a price increase would not be acceptable to the customers. Find the price at which the company should sell bagels in order to maximize its profit. Show all steps of the optimization task.

A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 24 per week at a price of $9 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 3 sales per week. (a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.) P(x) = (b) What price should the society charge for each feeder to maximize profits? $ What is the maximum weekly profit? $

Given the functional relationship: y = 14x5/x2  find the value of y when x = 1.5

AVC=10-0.03Q + 0.00005Q2TFC=60 What is the MC Function?

An electronics retailer wants to send codes for  $10  off a pair of headphones to the subscribers of its e-mail list. The coupon code will have two letters followed by three digits. The letters  A ,  B ,  C , and  D  and the digits  6  and  9  will not be used. So, there are  22  letters and  8  digits that will be used. Assume that the letters and digits can be repeated. How many such coupon codes can be generated? couponcodes