Hochpunkte, Tiefpunkte - Vorzeichenvergleich, 2. Ableitung - Vorzeichenwechselkriterium Wenn wir Extremstellen berechnet haben und auch schon ihre zugehörigen Extremwerte, so kann es immer noch sein, dass es sich gar nicht um Extrempunkte handelt. Denn eine Nullstelle der Ableitung kann auch nur Berührpunkt mit der x-Achse sein, in diesem Fall bliebe die Ableitung positiv (bzw. negativ) und die Steigung der Funktion bliebe positiv (bzw. negativ). Zur Überprüfung auf Hochpunkt bzw. 1. Vorzeichenvergleich Wir untersuchen die 1. Wenn der Vorzeichenvergleich um die Nullstelle ein Wechsel von positiv zu negativ zeigt, so handelt es sich bei dieser Nullstelle um eine Hochstelle der Funktion. Zweite Ableitung überprüfen Die Methode der zweiten Ableitung baut auf die des Vorzeichenvergleichs auf. Das Gleiche für einen Tiefpunkt. Und weiterhin ist klar, dass die zweite Ableitung in der hinreichenden Bedingung nicht Null sein darf. Extrempunkte auf Hochpunkt und Tiefpunkt untersuchen Gegeben sei die Funktion: Ihre erste Ableitung ist:
Google's AI Can Dream, and Here's What it Looks Like Software engineers at Google have been analyzing the 'dreams' of their computers. And it turns out that androids do dream of electric sheep... and also pig-snails, camel-birds and dog-fish. This conclusion has been made after testing the ability of Google's servers to recognize and create images of commonplace objects – for example, bananas and measuring cups. Google's artificial neural network creates its own images from keywords. So, what's the point in creating these bizarre images? The Google artificial neural network is like a computer brain, inspired by the central nervous system of animals. The Google team then realized that they could reverse the process. Sometimes, the resulting images are not quite what you'd expect... Google's artificial neural network's interpretation of a dumbbell. You may have noticed that no computer-generated dumbbell is complete without a muscular weightlifting arm. Highly detailed elements seem to pop up out of nowhere. [Via Google]
Videos Hans Rosling explains a very common misunderstanding about the world: That saving the poor children leads to overpopulation. Not only is it not right, it’s the other way around! The world might not be as bad as you might believe! Don’t Panic – is a one-hour long documentary produced by Wingspan Read more … Hans Rosling is debunking the River of Myths about the developing world. By measuring the progress in the once labeled “developing countries”, preventable child mortality can be history by the year 2030. Instead of studying history one year at the university, you can watch this video for less than five minutes. Explaining the global vaccination programs is NOT a party-killer! Is there a relation between religion, sex and the number of babies per woman? What was the greatest invention of the industrial revolution? Hans Rosling uses Gapminder bubbles in CNN Global Public Square to show US converge with other countries. A 55-minute documentary about Hans Rosling’s life & thoughts.
Smoothie Recipes For Everything Who knew that the solution to most our problems could be solved with a smoothie?! Smoothie Recipes For Everything infographic from Super Skinny Me gives you the ingredients and visually represents the amount of each that should put in. Trying to lose weight? Is there anything as versatile, adaptable and convenient as a smoothie? The major issue I have with this design is that the proportions visualized for each smoothie aren’t accurate to the recipe. Also, the actual amounts of each ingredient aren’t shown. Found on superskinnyme.com
Verfahrenstechnische Prozesse und Systeme Neben der Analyse von Verfahren, ihrer Zerlegung in Grundverfahren und deren Strukturierung entsprechend den Wirkprinzipien ist die Synthese von Verfahren, also das Zusammensetzen der Grundverfahren zu verfahrenstechnischen Systemen, in denen gewünschte neue Produkte hergestellt werden können, eine der Hauptaufgaben des Verfahrensingenieurs. Die Entwicklung eines neuen Verfahrens ist für ihn eine "Pioniersituation", da er einer Problemstellung gegenübersteht, die bisher nicht gelöst wurde. Neu sind nicht die zur Verfügung stehenden Grundverfahren und dafür bewährte konstruktive Lösungen, sondern das Neue besteht darin, daß die Grundverfahren aus einem alternativen Angebot auszuwählen und auf geeignete Weise zu verknüpfen sind. Unabhängig vom aufzubauenden System ist folgende Vorgehensweise kennzeichnend für die Verfahrensentwicklung: 1. 2. 3. Festlegung der konstruktiven Gestalt der Apparate/MaschinenErarbeitung eines Rohrleitungs- und Instrumentierungsfließbildes 4.
Visually stunning math concepts which are easy to explain Car maintenance and repair cost grapher This page helps you display and understand how much it has cost you to maintain and repair your car. You need to supply the data, which is just a list of amounts you paid for maintenance and repair and the odometer mileage at which the work was done. The analyzer spreads these costs out a bit and displays a record of how much the car has cost to maintain and repair over its life so far. This will help you compare cars to one another and will help you understand the way that repair costs come in as a car gets older. That may help you make a better decision about what to do with an older car. The analyzer is available here. We once had a nice, red Pontiac Grand Am. The first column shows odometer readings, the second column shows dollar amounts for maintenance (like oil changes) and repairs (like the head gasket replacement at 98,625 miles). The red line shows the average cost per mile, 6.46 cents per mile. Of course there is more to it than this. That's not so bad.
5 Thought-Provoking Quotes to Ponder Before the Week Commences - David Domzalski. So, I’m reading John Maxwell’s The 15 Invaluable Laws of Growth right now. I basically just started today with Chapter 1 and I wanted to share a few thoughts about it thus far. A few quotes Maxwell uses throughout this first chapter titled “The Law of Intentionality” really resonated with me. The first is from “The Boss” – Bruce Springsteen. “A time will come when you need to stop waiting for the man you want to become and start being the man you want to be.” The second quote Maxwell shares is called the Law of Diminishing Intent, which states: “The longer you wait to do something you should do now, the greater the odds that you will never actually do it.” Robert H. “What would you attempt to do if you knew you wouldn’t fail?” The fourth quote comes from author and professor Warren Bennis: “A mistake is simply another way of doing things.” Finally, the fifth quote I want to share with you comes from the legendary Jim Rohn: How do you feel after reading these quotes?
wait but why: Putting Time In Perspective Humans are good at a lot of things, but putting time in perspective is not one of them. It’s not our fault—the spans of time in human history, and even more so in natural history, are so vast compared to the span of our life and recent history that it’s almost impossible to get a handle on it. If the Earth formed at midnight and the present moment is the next midnight, 24 hours later, modern humans have been around since 11:59:59pm—1 second. And if human history itself spans 24 hours from one midnight to the next, 14 minutes represents the time since Christ. To try to grasp some perspective, I mapped out the history of time as a series of growing timelines—each timeline contains all the previous timelines (colors will help you see which timelines are which). All timeline lengths are exactly accurate to the amount of time they’re expressing. A note on dates: When it comes to the far-back past, most of the dates we know are the subject of ongoing debate.
Beautiful Mathematical GIFs Will Mesmerize You Digital artist and physics PhD student Dave Whyte is dazzling our computer screens with his mesmerizing GIFs that are the perfect marriage of mathematics and art. And we can’t stop watching them. Whyte shares his brilliant, procrastination-fueling creations on an almost daily basis on his Tumblr account, Bees & Bombs. Whyte studies the physics of foam and told Colossal that his first geometric GIFs riffed on computational modules that he was exploring as an undergraduate student. To create his eye catching animations, Whyte uses a programming language called Processing. Check some of them out here (caution: may induce serious time wasting): [Via Colossal, io9 and Bees & Bombs]
255Tbps: World’s fastest network could carry all of the internet’s traffic on a single fiber A joint group of researchers from the Netherlands and the US have smashed the world speed record for a fiber network, pushing 255 terabits per second down a single strand of glass fiber. This is equivalent to around 32 terabytes per second — enough to transfer a 1GB movie in 31.25 microseconds (0.03 milliseconds), or alternatively, the entire contents of your 1TB hard drive in about 31 milliseconds. To put 255Tbps into perspective, the fastest single-fiber links in commercial operation top out at 100Gbps, or 2,550 times slower. 255Tbps is mindbogglingly quick; it’s greater, by far, than the total capacity of every cable — hundreds of glass fibers — currently spanning the Atlantic Ocean. In fact, 255 terabits per second is similar to — or maybe even more than — the total sum of all traffic flowing across the internet at peak time. How did the researchers at Eindhoven University of Technology (TU/e) and University of Central Florida (CREOL) do it?
18 Useful Kitchen Hacks To Make Your Life Easier Did you know you can easily half an apple without a knife and without knowing any special Kung Fu tricks? Or that you can pit a cherry using a chopstick and a beer bottle? One of the great things about the internet is the way everyone can share their tricks and shortcuts that make life that little bit easier. Cook bacon in a waffle maker. Ripen bananas quickly by popping them in the oven for 30 minutes at 300 degrees. Clean your microwave quickly & easily with this simple tip. DIYManiacs Use a melon baller to remove pumpkin seeds. Press a hole in your burger so it cooks evenly. Whip cream by shaking it in a jar. Grate butter to soften it. Use a rubber band to loosen a tight jar lid. Coat measuring cups with a spray of cooking oil to avoid a sticky mess. Put marshmallows on your cupcakes five minutes before they're cooked for a quick and easy icing solution. Open a beer or coke with only a dollar bill. Peel a potato with only your bare hands. Peel garlic in seconds. The easiest way to pit a cherry.