Calculus Answers

Find the point on the line -6 x + 6 y + 3 =0 which is closest to the point ( -4, 3 ).

The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 396 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 3 dollar increase in rent. Similarly, one additional unit will be occupied for each 3 dollar decrease in rent. What rent should the manager charge to maximize revenue?

if y=e^ax cos^3 x sin^2 x.find dy/dxif y=e^ax cos^3 x sin^2 x.find dy/dx

How to compare the following numbers without using the calculator?
√5-√3 and √(8-2√15)

A box with a square base and open top must have a volume of 364500 cm3. Find the dimensions of the box that minimize the amount of material used.

the temperature of a vase is 1,080 degrees F to begin with, and the temperature of the room with the cooling table it is placed on is 80 degrees F. 4 minutes later, the temperature of the vase is 830 degrees F. Find a formula for the temperature of the vase after t minutes.

If g(x)=f(b+mx)+f(b-mx), where f is differentiable at b, find g'(0)

Suppose that a when a cell phone store charges 16$ for a car charger, it sells 125 units. When it drops the price to 15$ it sells 130 units. Assume that demand is a linear function of price. If each phone charger costs 1$ to make, what price should the store charge to maximize its profit?
If x is the number of times the price is reduced by one dollar. Find a function for total profit with respect to x. A negative value for x will mean the price is increased.
f(x)=?
Price to maximize profit =?

Chocolates are sold in a store. The shop owner declared that if someone buys for 6 to 10
chocolates, he will give a discount of 1 taka on each chocolate. If someone buys from 11
to 15 chocolates, he’ll give a further discount of 1 taka on each chocolate. But it will
always cost you more as you buy more chocolates. If you decide to buy 3 chocolates from
that store, what is the minimum amount of money you need to spend?

Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)
f ''(x) = 8 + x3 + x5