Question

Find the x values of all inflection points of f.
Inflection points of f occur at x =
Note: If there are no such points, enter "none". If there is more than one, enter the x-values as a comma-separated list, e.g. 1, 2

Answer 1

not really sure how to find inflection points

f''(x)=(2 (-1+3 x^2))/(7 (1+x^2)^3)

Answer 2

@radar can you give me a hand?

Answer 3

@etemplin can u help?

Answer 4

a point on a curve at which the second derivative changes sign. you have the second derivative. now set it equal to 0, find the roots of it, and make a number line, label the roots, and determine if in those sections between roots the function is positive or negative. if it changes sign at a root, its an inflectio point

Answer 5

Zeros of f′′(x) at x=-1/sqrt3,1/sqrt3
f′′(x) not defined or not continuous at x=none
f is concave up on the following intervals:(-inf,-1/sqrt3)U(1/sqrt3,inf)
f is concave down on the following intervals:(-1/sqrt3,1/sqrt3)

Answer 6

at the points where it changes concavity, thats an inflection point

Answer 7

so (-1/sqrt3), and (1/sqrt3)

Answer 8

as long as we did our work right, yes, those are the answers

Answer 9

this is what it tells me
Your answer isn't a number (it looks like a list of numbers)

Answer 10

what if you change them to fractional exponents? or approximate decimals?

Answer 11

it would still be listing numbers

Answer 12

not a big deal if you dont know, but all my other answers are correct

Answer 13

it told you to put them in a list tho

Answer 14

ya this program is stupid like that

Answer 15

agreed

Answer 16

so you dont have any other ideas?

Answer 17

hmmm...im wondering if one of them is an asymptote...then it wouldnt be a point of inflection (i dont think)

Answer 18

it doesnt look like any of them are tho

Answer 19

i tried both of them separately and didnt work either

Answer 20

hmmmm

Answer 21

@hartnn could you give us a hand here

Answer 22

another question how do i know if i need to find the derivative or the second derivative?

Answer 23

depends what youre looking for...therss some stuff that you need the first derivative (slope) and others that you need the second (concavity/inflection). i currently dont remember all the tests that go with each one, but if you give me a few mins, i can find a link that shows all of them

Answer 24

lets say this x/(8x^2+6)

Answer 25

what do you need to find?

Answer 26

let me rephrase: what information do you need to find?

Answer 27

List the x values of the inflection points of f. If there are no inflection points, enter 'NONE'.

Inflection points of f occur at x=

Answer 28

you need the second derivative

Answer 29

ok, and to figure out how to find the inflection point lol

Answer 30

you need to find the zeroes of the second derivative, and make a "sign chart" based on the second derivative. if the signs change at a critical point, you have a point of inflection there

Answer 31

do i plug these into the origional equation?

Answer 32

no. into the second derivative. you need to find where the second derivative changes sign