can someone help me out on some calculus?

- anonymous

can someone help me out on some calculus?

- Stacey Warren - Expert brainly.com

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- anonymous

what's your question ^_^?

- anonymous

im doing second derivatives and graphing and i am totally lost

- anonymous

how come? which part are you lost in?

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## More answers

- anonymous

something that has to do with infelction points? :)

- anonymous

inflection*

- anonymous

this problem..summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y=f(x)
f(x)=(x-2)(x^2-4x-8)

- anonymous

i have no idea what to do. or where to start

- anonymous

does it have to do with graphing f'(x)?

- anonymous

it's in the lesson of second deriviatives and graphing

- anonymous

so it has to do with inflection points :)because when you find the second derivative, you are finding, at the same time, the inflection points, where does the curve change, does it open up or down ^_^

- anonymous

it starts opening down them switches and opens up

- anonymous

excellent, so you have found the inflection points, can you compute the integral? Where does it start opening up + end + same with down? :)

- anonymous

okay so how do i find the exact point it changes. its -\[\infty\] starting then it turns and goes up

- anonymous

make a table putting the following:
x| ( put the points you have found, Inflection points) then check what happens to f(x) when you substitute them in the function ^_^ is it (-)? (decreasing)? or (+)? (increasing)? ^_^ so if it's positive then it's opening upwards, and the vise versa ^_^
_____________________________________________
f(x)|
_____________________________________________
f''(x)|

- anonymous

then from the x points you can see from where and where does it open upwards or downwards ^_^

- anonymous

can you give me an example like (0,16)

- anonymous

those are the x points?

- anonymous

no 0 is an x point

- anonymous

the y of that is 16 according to my calculator

- anonymous

by tracing the graph

- anonymous

wait, are you having trouble drawing the function?

- anonymous

no

- anonymous

lol, I'm sorry, I'm confused too ^^"

- anonymous

what's does your question really say?

- anonymous

for the answer in the back of the book it says:
domain:all real numbers
y int.: 16
x int. \[2-\sqrt{3}, 2, 2+2\sqrt{3}\]
increasing on: (-\[\infty,0) and (4,\infty)\]
decreasing on (0,4)
local maximum at x+0, local minimum at x+4
concaved downward on (-\[\infty\], 2)
concaved upward on (2, \[\infty\])
inflection pointat x+2

- anonymous

im just trying to figure out how to get those things

- anonymous

Alright, I got the question, they want you to find the critical points, increasing and decreasing intervals, inflection points, intervals of concavity, domain and range lol :)

- anonymous

yes

- anonymous

now i have no clue how to get that

- anonymous

Now for the domain and range, since you'r function is a polunomial then the domain + range = :
\[(-\infty , \infty)\]
2) To find the critical numbers you've got to derive the function once then take 2 conditions for f'(x) to find the critical numbers
a) f'(x) = 0
b) f'(x) = undefined
For your question, for all x, x is defined :) , so you'll take condition (a), in this case, f'(x) = 0, then you can find the zeros of your function.
Those zeros are your critical numbers.
3) To find the critical points, you have to draw a table, like the one I have showed you before, but instead of f''(x) it's going to be f'(x) and put the critical numbers in the table and the substitute them in the original function to check if you're going to get a (-) value = decreasing, or a (+) value = increasing.
5) For the inflection numbers, you have to derive once more and take the zeros of the function, same condition for f'(x) ^_^ so those zeros will be your inflection numbers
6) Put these numbers in the table, (the same one I have showed you above) or just put numbers - (any number) 0 and ( + any positive number) then substitute them in the original function to see whether you're getting a + value or negative. + = concaved up, - = concaved down
7) finally just put all the calculations you have found and translate it into a graph
These are the steps ^_^ good luck

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