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AP Calc 3.4b: Second Derivative Test

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everybody Welcome to 3.4 Part B we're going to write is it really what the second derivative test is in math speak function such that F Prime of the open intervals if you evaluate your second derivative at these critical numbers if you have a relative minimum value if you'd rivet event- Max at that value and here's an important note evaluate your second derivative at that critical number and then you can't use this test to find extrema reminder for the first derivative test and another test to find extrema I want to see the difference between a second and the first derivative test bright color here and we're going to how to draw a Venn diagram a big circle here Circle good thing I'm not okay so let's talk I'm going to stay and blue II Olympic black but they don't help us find they both Brandy creamer you can use to find extrema and do birds use the first derivative at zero wherever the first derivative zero those are critical number when does the cricket numbers for both of these tests and both can find extrema here are some differences Happy Birthday written test Wii U a text number from incredible right that's what we do with the first derivative test and look to the left and the right of the critical number when they use the first derivative test what the second derivative test is different we are that Empire point so the second derivative test evaluate right up the critical number it doesn't make any bold you can occur evaluate the exact number to be come up with and thanks for the second derivative test doesn't look to the left or the right it looks to see what exactly is happening at that point and then we determine monster man from that value so I guess I could have made that smaller but that's okay these are the differences and here's what's the same temperature in example of that a question going to ask her to find the relative Trina I'm at equals -3x to the 5th power + 5 x q is going to help you guys first directions to First find the first derivative and then find the second derivative and go from there so the first -15 x to the fourth 15 x squared and my second derivative is going to be -60 X cubed plus 30X okay remember flat definition at the front of that make a derivative so what I'm going to do tricks on my credit card number and I'm going to start my first derivative equal to 0 at the same time so when I talk to her excuse my first derivative of x squared minus 1 as a factor Infamous I can determine that the zeros the critical numbers are going to be at equals 0 and 1x equal -1 and I like you and I kept getting back into my second but I'm not interested in the number of my original function values on my original function as what I'd like to do determine what's going on what are back on on the far will call these the point will call then turn double crime event Quinceaneras are going to be late we're off of negative 1 0 and where it is positive what I'm going to do right now and I am going to explain how I'm getting there I'm getting the Y value by my back to my original function and when you do not talk later calculator work at this point zero and not interested in what's happening here with my second derivative and when I pick value I get a positive value when I take zero and I substituted into my second derivative I get 0 and when I take one and I spoke to you then I get a negative number so what I've got going on here if I look at my second derivative test description second derivative I have a minimum I have a minimum here when am I my second derivative alright so far a game at the point 0 0 so what I can do that little note that you to evaluate what's going on with your phone my first derivative test and I know what's happening at negative negative I need to look at the call this is the first derivative test and I'm interested now looking at scary guy having my first derivative test -1 -1 to 0 0 deposit one I want to know what's happening in those intervals so good test numbers negative and positive 1/2 but if I take those numbers and I saw my first derivative what I do is a positive number and another positive number so it doesn't really help me not much Happening Here I can see what's happening I can feel it from -1 no I don't have a Mac torrent 00 Bears no extrema 00 and what we can instead that has a relative map one and a relative men -1 - 2 how to better understand what's going on here so we can have a fire going and we're going to graph the original function we're going to grab that -3x V where is X to the Third we can be very confusing and supported here Museum all right here is that .00 we can see that our graph increases increases and kind of takes a break for a second but can't even though another example answer the question find the relative extrema find the relative extrema 2 x to the fourth minus 16 x squared good way to start into for fun and I would get 8/3 - 32 x my first service information second derivative my ex double Prime of X I would get 24 x squared minus alright again we're going to identify those critical number phone number happen where a prime is zero I'm going to 4 as a factor now I can clearly see that microphone numbers are going to happen it is zero and at 5:30 - 2 no it's my job and create the value the number happening on my original function at the exact value I could see that sell you and I spoke to come back into my original function and when I do that I get the following coordinates -2, -3 to 0, 0 into -32 again highlight how it came across as valued to ask you a question alright I got these boys from the 10 my credit card number Computing and Creek phone number you know what number and when we do that when I put in negative two to my second derivative call Nick value when I take an arrow and I put it into my second derivative it's not going to change the sign to its going to say and remember president is greater than I have a relative men minimum and if it's negative phone number and again positive means a minimum of how I would report my answer I would say that relative minimum men point -2 - 32 + 2 + -32 and as a relative maximum 00 and I guess you're at the point where I can't wait to see you in class tomorrow

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AP Calc 3.4b: Second Derivative Test

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