In one sentence, describe what the following article is about: 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)=500q−150q2{\displaystyle R(q)=500q-{\frac {1}{50}}q^{2}}. The first derivative, therefore, is: R′(q)=500−250q{\displaystyle R^{\prime }(q)=500-{\frac {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)=500−250q{\displaystyle R^{\prime }(q)=500-{\frac {2}{50}}q} 0=500−250q{\displaystyle 0=500-{\frac {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=500−250q{\displaystyle 0=500-{\frac {2}{50}}q} 250q=500{\displaystyle {\frac {2}{50}}q=500} 150q=250{\displaystyle {\frac {1}{50}}q=250} q=50∗250{\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=500−150q{\displaystyle p=500-{\frac {1}{50}}q} p=500−15012,500{\displaystyle p=500-{\frac {1}{50}}12,500} p=500−250{\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=p∗q{\displaystyle R=p*q}. The maximum revenue for this example, therefore, is:  R=p∗q{\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.
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.

In one sentence, describe what the following article is about: Your water might naturally break at the beginning or during your labor. A lot of people expect a large gush of fluid, but you might have a different experience. In addition to a gush, you could also experience a feeling of wetness in your vagina or frequent leaking of small amounts of liquid from your vagina. If you're not already in labor, it will likely begin after your water breaks. Get ready to follow your birth plan. If you're going to the hospital, for example, grab your bag and head out the door. Ask for help if you need a ride or other assistance. Wherever you plan to give birth, you should let your healthcare provider know that your water broke. They will likely ask you some questions and give you some instructions. If you're not sure if your water has broken or not, you can still give them a call and describe what you are experiencing. Labor should begin shortly after your water breaks, in most cases. But if it doesn't, your healthcare professional can help you. If labor hasn't begun within 24 hours, you will likely be offered an induction. This might seem scary, but try not to worry. Inducing labor is really common. It can be really helpful because without fluids in the amniotic sac, your baby will be at higher risk for infection. Your doctor might also induce if either you or your baby is suffering from a medical condition such as:  Hypertension Preeclampsia Gestational diabetes Bleeding during pregnancy  Your doctor might induce labor by inserting synthetic prostaglandins into your vagina, which can soften the cervix. They might also induce by starting an intravenous medication such as Pitocin. This will cause the uterus to contract.
Summary: Learn the signs of water breaking. Expect labor to start soon, in most cases. Call your doctor or midwife. Get induced if labor does not begin.

In one sentence, describe what the following article is about: If you are buying a house, ask the seller what company they used to inspect the home, to ensure that you choose a different one.  This is important in cases of fraud or deception, which are rare but still possible. For example, the seller could have a personal relationship with the inspector and ask them to refrain from disclosing important information. It is also important because its always a good idea to have two separate, unbiased, and impartial inspections done from two different perspectives to ensure that nothing major is overlooked. " This is a simple way to find companies with websites or companies listed in online yellow pages.  Keep in mind that the first several results of a Google or similar search engine query will be paid advertisements, and not necessarily the best companies. Scroll through the results to see your options. You can also try an old fashioned phone book if you have one handy! Anyone who has purchased a home in the last couple of years in your town will do, but especially ask friends who have purchased similar homes (age, condition, location).  Post to social media accounts like Facebook or Twitter. Often you may not know of anyone who has used a service, but your trusted friends might post your query to their own friends and find someone who can give a recommendation. Keep in mind that if you are buying a house, its common for the real estate company you are using to recommend an inspection company. Do not automatically assume this company will be a good one. After you've found a few local options, look for reviews on websites other than their own, as many companies edit the reviews on their own websites or only post positive ones. You can also find reviews on social media business pages, if you know the name of a particular company. Keep in mind that very small businesses often only have reviews written by friends or family of the owners, who may have never used their services. This isn't necessarily a reason to reject them out of hand, but you may need to do a little more digging to find actual clients.
Summary:
Find out what company the other party is using. Google your town and the phrase "home inspection company. Ask friends in the area. Google them and read reviews.