Calculus Answers

A manufacturer has found that marginal costs are 3𝑞 2 − 60𝑞 + 400 dollars per unit when q units have been produced. The total costs of producing the first 2 units are $ 900. What is the total cost of producing the first 5 units?

a ladder 20 feet long leans against a vertical building is the tower of the ladder slides down at a rate of p3 fits how fast is the bottom of the ladder sliding away from the building in the top of the ladder is 10 feet above the ground

∫ 3𝑥 + 6 √2𝑥 2 + 8𝑥 + 3 𝑑x

When the price of a certain commodity is p dollars per unit, the manufacturer is willing to supply x thousand units, where 𝑥 2 − 2𝑥√𝑃 − 𝑃 3 = 31 How fast is the supply changing the price when the price is $ 9 per unit and increasing at the rate of 20 cents per week 

Suppose the output at a certain factory is 𝑄 = 2𝑥 3 + 𝑥 2𝑦 + 𝑦 2 units, where 𝑥 is the number of hours of skilled labour used and 𝑦 is the number of hours of unskilled labour. The current labour force consists of 30 hours of skilled labour and 20 hours of unskilled labour. Use calculus to estimate the change in unskilled labour y that should be made to offset a 1-hour increase in skilled labour x so that output will be maintained at its current level

Find 𝑑𝑦 𝑑𝑥 if 𝑥 2𝑦 + 2𝑦 3 = 3𝑥 + 2𝑦

An environmental study of a certain suburban community suggests that its average daily level of carbon monoxide will be 𝐶(𝑓) = √0.5𝑝 2 + 17 Parts per million when the population is p thousand. It is estimated that t years from now, the population of the community will be 𝑝(𝑡) = 3.1 + 0.1𝑡 2 thousand. At what rate will the carbon monoxide level be changing with respect to time 3 years from now?

Differentiate the function 𝑓(𝑥) = (3𝑥 + 1) 4 (2𝑥 − 1) 5 and simplify your answer

Find 𝑑𝑦 𝑑𝑥 if 𝑦 = 𝑢 3 − 3𝑢 2 + 1 and 𝑢 = 𝑥 2 + 2