In calculus, the derivative of any function is used to find the rate of change of that function. The maximum value of a given function occurs when the derivative equals zero. So, to maximize the revenue, find the first derivative of the revenue function. Suppose the revenue function, in terms of number of units sold, is R(q)=500q150q2{\displaystyle R(q)=500q-{
rac {1}{50}}q^{2}}. The first derivative, therefore, is: R(q)=500250q{\displaystyle R^{\prime }(q)=500-{
rac {2}{50}}q} For a review of derivatives, see the wikiHow article on how to Take Derivatives. When the derivative is zero, the graph of the original function is at either a peak or a trough. This will be either the maximum or minimum value. For some higher level functions, there may be more than one solution to the zero derivative, but not a basic price-demand function. R(q)=500250q{\displaystyle R^{\prime }(q)=500-{
rac {2}{50}}q} 0=500250q{\displaystyle 0=500-{
rac {2}{50}}q} Use basic algebra to solve the derivative for the number of items to sell where the derivative is equal to zero. This will give you the number of items that will maximize the revenue. 0=500250q{\displaystyle 0=500-{
rac {2}{50}}q} 250q=500{\displaystyle {
rac {2}{50}}q=500} 150q=250{\displaystyle {
rac {1}{50}}q=250} q=50250{\displaystyle q=50*250} q=12,500{\displaystyle q=12,500} Using the optimal number of sales from the derivative calculation, you can enter that value into the original price formula to find the optimal price. p=500150q{\displaystyle p=500-{
rac {1}{50}}q} p=50015012,500{\displaystyle p=500-{
rac {1}{50}}12,500} p=500250{\displaystyle p=500-250} p=250{\displaystyle p=250} After you have found the optimal number of sales and the optimal price, multiply them to find the maximum revenue. Recall that R=pq{\displaystyle R=p*q}. The maximum revenue for this example, therefore, is: R=pq{\displaystyle R=p*q} R=(250)(12,500){\displaystyle R=(250)(12,500)} R=3,125,000{\displaystyle R=3,125,000} Based on these calculations, the optimal number of units to sell is 12,500, at the optimal price of $250 each. This will result in a maximum revenue, for this sample problem, of $3,125,000.
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One-sentence summary -- Find the first derivative of the revenue function. Set the derivative equal to 0. Solve for the number of items at the 0 value. Calculate the maximum price. Combine the results to calculate maximum revenue. Summarize the results.

The delegate should login to their personal Gmail account through a standard desktop browser, as email delegation cannot be accessed via Gmail's iOS or Android application. It will contain a request for you to accept the delegation. Doing so will activate the delegation. Confirmation and verification for the delegate may take up to half an hour. You'll find it in the upper right hand of your browser window. It will now appear under your own. You can now read and compose emails on behalf of the other user.
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One-sentence summary -- Login to your Gmail account. Click on the e-mail sent by the Gmail Team. Tap on the confirmation link provided. Click on your profile picture. Tap on the delegated account.

If you send the carcasses to the veterinarian for testing, they will dispose of the deceased animals after they perform their tests on them. Depending on their facilities, they may incinerate or bury the animals. You may also request the remains if you want to dispose of the animals yourself. Typically, the vet will dispose of any dead animals for free after performing a necropsy. If you do not contact your veterinarian and are unsure about how to dispose the dead animals, call your local animal control. They will help you determine the best way of disposing of the carcasses. You can also take the dead puppies to your local animal services center and see if they will dispose of them for you. your puppies. In most places, you can bury deceased animals on your own property. If you have small children, you may want to have a small burial ceremony to help them deal with the death. For something as small as a puppy, a shoebox should work as a coffin. You should bury the dead animal at least two feet (61 cm) deep to prevent scavengers from digging it up. Be sure to find out what your local rules and regulations are before burying the deceased animals. You may also want to explore the option of burying the animals in a pet cemetery. If you feel particularly attached to the dead puppies, you can also look into having them cremated and keeping their ashes in an urn.
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One-sentence summary -- Let the veterinarian dispose of them. Contact animal control. Bury

If you have a Canon printer which uses a FINE cartridge like in the MX or MG series, you will have a center paper output cover which is above your output tray. Open your ink tray in the center which is above the output tray. Make sure that your printer is plugged in and turned on. In order for the ink compartments to slide into view, your printer must be powered on. The ink cartridges will slide to the right side of your open tray. This is the replacement position. In some Canon printers, such as the MX or MG Series which uses FINE ink cartridges, the cartridge holder moves to a replacement position behind the head cover. The head cover will open automatically. If you have a Canon PIXMA printer which uses several, smaller ink cartridges, the cartridge holder will slide into the middle of your operations tray when you open the operation lid on top of the printer. If there are already ink cartridges in your printer, you will have to remove these old ones. Press down on the ink cartridge you want to remove. The cartridge lock lever will click, dislodging the cartridge. Once you hear the click and see the existing ink cartridge popped out, pull it the rest of the way out. Take the new cartridge from its packaging and remove the protective tape. Some Canon printers only use two cartridges, one black, and one tri-color, such as in the MX series. Others like the PIXMA use several cartridges, one for each color. All cartridges will have a protective film over the ink nozzle you need to remove. Remove the protective tab on the ink cartridge. This is a plastic film that covers the part of your cartridge which dispels the ink. Be careful not to touch the copper-colored area of the cartridge or the ink nozzles. touching this area can cause clogs, ink failure, or a disconnection if your fingerprints smudge the area. Do not shake your cartridges either. Gently slide the new cartridge into the ink slot. Insert your cartridge into the slot with the ink nozzles facing away from you. The color cartridge(s) goes on the left side. The black cartridge on the right side. Make sure you hear a click to ensure the cartridge is locked into place. You should feel it click into place. Once the door is closed properly you will hear the cartridges slide back into place. Finished.
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One-sentence summary --
Open the ink tray in the center of your printer. Remove any existing ink cartridges from the printer. Remove the new ink cartridge from the packaging. Insert your new ink cartridges. Close the ink cartridge door.