Question

find the max value of f''(x)
f(x)=1/(x^2+1) interval [0,3]

Answer 1

do i have to find the derivative first?

Answer 2

i guess you have to find the derivative twice

Answer 3

yes, the '' part, correct?

Answer 4

but it is not hard if you write it as
\[f(x)=(x^2+1)^{-1}\] and use the chain rule

Answer 5

a tutor mentioned when there is two '' signs in the f(x) function, i have to find the derivative 3 times, what do you think?

Answer 6

yes

Answer 7

first derivative is \[-2x(x^2+1)^{-2}\]

Answer 8

no i do not think so

Answer 9

No that is the second derivative. You only need to take the derivative twice

Answer 10

first derivative if \(f'\) second derivative is \(f''\)

Answer 11

yes, i got that for my first derivative. for my second derivative i got, -4x(x^2+1)^-3

Answer 12

this is because u have to check where the third derivative of function goes zeri so that such point where it goes zero will denote point of extremum of second derivative

Answer 13

ooooh i see hold the phone
to answer the question above, find the max of \(f''\) then yes, you need the third derivative to find the max of the second derivative

Answer 14

what @thinker said

Answer 15

yay :D

Answer 16

so! onto the second derivative!

Answer 17

we use the product rule to find the second derivative, right?

Answer 18

i have my work written all over the place so i have to redo my problem from yesterday

Answer 19

but first you need the second derivative, which i think is
\[\frac{8x}{(x^2+1)^3}\]

Answer 20

i would write the first derivative as
\[\frac{-2x}{(x^2+1)^2}\] and then take the derivative of that

Answer 21

you are going to have to add them up anyway, so rather than use the product rule it is going to be best to use the quotient rule, then you don't have to add the expressions, you already have it as a quotient
your final job is going to be to find the zeros of the third derivative, so you need it in fraction form

Answer 22

ok, so i'll use the quotient rule, brb while i do this

Answer 23

ok do some algebra to simplify also, and you can check it with the answer i wrote above