Question

f(x)=x sqrt(x^2 + 3) + 9
find f'(1) and f''(1).

now find the value of x where the 2nd derivative equals zero. (that is, solve the equation f''(x)=0 for x.)
x=

Answer 1

help?

Answer 2

someones helping me! ahhh!

Answer 3

http://openstudy.com/study#/updates/4f4fcca5e4b019d0ebaef38c
i need help with this too

Answer 4

\[f(x)=x \sqrt{(x^2 + 3)} + 9\]
\[f'(x)=(x ^{2}+3)^{1/2}+\frac{x ^{2}}{(x ^{2}+3)^{1/2}}\]
\[f'(1)=\frac{5}{2}\]

Answer 5

what about the other 2?

Answer 6

Differentiate f '(x) again, then equate f ''(x)=0

Answer 7

\[f''(x)=\frac{x}{(x ^{2}+3)^{1/2}}+\frac{x(x ^{2}+6)}{(x ^{2}+3)^{3/2}}\]

Answer 8

f''(x)=0, then solve for x

Answer 9

can f''(x) be written any other way

Answer 10

@amistre64 seeing if i can ping myself here

Answer 11

huh?

Answer 12

i couldnt find the post, and pinging myself had no effect ...

Answer 13

@mariomintchev is a ping that sends you a link to where you ping it at

Answer 14

alot easier to follow to then a link in a fan testy

Answer 15

writting f'' in another way doesnt change the math; so going thru all the extra work to "simplify" is usually a lost cause

Answer 16

my site isnt accepting my answer

Answer 17

help?

Answer 18

i am lost. which part is needed? second deriviative?

Answer 19

yes. everything else i have.

Answer 20

well i need the first derivative first

Answer 21

5/2

Answer 22

\[\frac{2x^2+3}{\sqrt{x^2+3}}\] if i am not mistaken

Answer 23

i mean that is the first derivative. second one in a minute

Answer 24

keep going

Answer 25

\[\frac{x(2x^2+9)}{(x^2+3)^{\frac{3}{2}}}\]

Answer 26

now this will only by zero if x = 0

Answer 27

since
\[2x^2+9\geq 9\] so that part is never zero

Answer 28

that should do it right?

Answer 29

it keeps saying its wrong. maybe im putting it in wrong. idk but im going nuts.

Answer 30

use the wolf ;)

Answer 31

http://www.wolframalpha.com/input/?i=2nd+derivative+%28x*sqrt%28x%5E2+%2B+3%29+%2B+9%29

Answer 32

the dirigible is right

Answer 33

its not accepting that answer

Answer 34

make sure youve given us the correct f(x)

Answer 35

retype it for us

Answer 36

what SAM has above is correct. that is what the problem looks like

Answer 37

and you say it wasnts f'(1) and f''(1) right?

Answer 38

scroll up ^^^^

Answer 39

yes

Answer 40

for f'(1) its 5/2.

Answer 41

yes

Answer 42

f''(1) = 11/8

Answer 43

o my god! yes! please show me how you got that

Answer 44

http://www.wolframalpha.com/input/?i=2nd+derivative+%28x*sqrt%28x%5E2+%2B+3%29+%2B+9%29%2C+x%3D1

you just plug in x=1 into f''

Answer 45

\[\frac{1(2(1)^2+9)}{((1)^2+3)^{\frac{3}{2}}}\]
\[\frac{11 }{(4)^{\frac{3}{2}}}\]
\[\frac{11 }{(64)^{\frac{1}{2}}}\]
\[\frac{11 }{8}\]

Answer 46

ok ur awesome! need a final answer for 2 more problems like this so if u could give me a hand that would be sweet!

Answer 47

i already posted them long ago. i just dont have a final answer.

Answer 48

http://openstudy.com/study#/updates/4f4fcca5e4b019d0ebaef38c

Answer 49

http://openstudy.com/study#/updates/4f4fb411e4b019d0ebaee20d