Question

can someone help me out on some calculus?

Answer 1

what's your question ^_^?

Answer 2

im doing second derivatives and graphing and i am totally lost

Answer 3

how come? which part are you lost in?

Answer 4

something that has to do with infelction points? :)

Answer 5

inflection*

Answer 6

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)

Answer 7

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

Answer 8

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

Answer 9

it's in the lesson of second deriviatives and graphing

Answer 10

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 ^_^

Answer 11

it starts opening down them switches and opens up

Answer 12

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

Answer 13

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

Answer 14

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)|

Answer 15

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

Answer 16

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

Answer 17

those are the x points?

Answer 18

no 0 is an x point

Answer 19

the y of that is 16 according to my calculator

Answer 20

by tracing the graph

Answer 21

wait, are you having trouble drawing the function?

Answer 22

no

Answer 23

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

Answer 24

what's does your question really say?

Answer 25

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

Answer 26

im just trying to figure out how to get those things

Answer 27

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 :)

Answer 28

yes

Answer 29

now i have no clue how to get that

Answer 30

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