this week in calculus we learned more about first derivatives and second derivatives. i understand more about first derivatives such as the steps:
Steps are as follows:1. Take the derivative2. Set = 03. Solve or x =>max & min (extrema), horiz tangent4. Set up intervals using step 5. plug in 1st derivative6. To find an absolute max/min plug values from #5 into original function. Check endpoints. i also under stand concavities (concave up/ concave down)1st derivative: Positive slope, Negative slope, horizontal tangent 2nd derivative: Concave up, Concave down, point of inflection. if the function is concave up it is positive and above the axis and if its concave down its negative and below the axis. since i wasnt in class for the stuff on second derivatives i still dont understand that. so if anyone can help me that would be good. i understand how to get the first derivative but not the second. Maximum-original, Minimum-orignial, Extrema. i dont think i was there for that either so i need help with that too. And can someone explain an extrema for me?
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okay, if you get how to get the first derivative then you really do know how to get the second.
ReplyDeleteit's just taking the derivative of the first derivative that you got!
so if you have:
x^3+x^2+20
your first derivative will be:
3x^2+2x
so for your second derivatve you will get:
6x+2
THAT'S IT!
however, for the hard .. or really big ones .. i don't understand that so well either, sorry, but i hope this helps!
Yeah, I was confused about the second derivative too until I realized it was almost the same as the first derivative. Like Ellie said you take the derivative of the derivate and then set equal to zero. Also, for your intervals it is the same thing too except positive would be concave up and negative would be concave down. That gives you your point of inflection and your maxs and mins. I'm pretty sure an extrema is just another word for your maxs and mins.
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