Okay, I wasn't at school monday or tuesday, and on wednesday there was that test... so I can only really write about what happened thursday and friday. By the way, this thing is probably going to suck because i'm rushing it because I have like no time and I forgot about it and I thought we had an extra day because tomorrow is labor day.
First, we started with vocab words, such as: increasing, decreasing, positive slope, negative slope, concave up, concave down, horizontal tangent, derivative above axis, derivative below axis, zero of derivative, maximum, minimum, and point of inflection.
First derivative test
increasing decreasing, horizontal tangent, max/min
to work this problem, you need to
take a derivitive,
set = to 0
solve for x to get max, min, horizontal tangents, extrema.
Set up intervals using step 3
plug in first derivative
to find an absolute max/min plug values from step 5 into the original function
EXAMPLE
f(x)=1.2x-sinx. Find the relative extrema of f(x) on the interval (0,2pie).
the derivative is 1/2-cos(x)
set that = to zero, so you get 1/2cos(x)=0, then cosx=1/2, then x= (cos^-1)(1/2), so then you get your critical points, which are (pie/3), and (5pie/3)
Then let's say it asked you to find the relative max's and mins
you use the points, (0, pie/3) (pie/3, 5pie/3) and (5pie/3, 2pie)
after you plug in the first one, you find out it's negative, so it's decreasing
the second one is positive, so it's increasing
the third one is decreasing
so your min=(pie/3)
and your max is (5pie/3)
this is probably a dumb question, but, one thing i don't understand is the different derivative things, like 1st, or 2nd derivative or whatever. i know in the example above it only involved the first derivative, so what exactly would a second derivative be used for? and what exactly is it?
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ReplyDeletei added a question because it didn't have one before.
ReplyDeleteOriginal deals with Increasing, Decreasing, Maximum, and Minimum
ReplyDeleteFirst Derivative goes with Positive slope, negative slope, and Horizontal Tangent
Second Derivative is for Concave Up and Concave down
And the rest>>Derivative above axis ( positive slope and concave up), Derivative below axis (negative slope, and concave down), and Zero of derivative (horizontal tangent, and negative slope)
BUTTT...the first derivative is basically the graph of the derivative of the graph that you're looking at [or the equation].
The second derivative is .. like the derivative of the derivative...I THINK??...
cause like if you have x to the 3rd it would be like a "N" on the graph...[kinda], but when you take the second derivative it'll be like a parabola...[which is like x squared]
hope i helped!
I don't think the 2nd derivative is the derivative of the derviative. I thought she said you can acutally take many derivatives of a graph. So it is just another derivative.
ReplyDeletewell i just got like two different answers lol. i'm clueless.
ReplyDelete