Question

x^3sqrt(x-9) find critical numbers

Answer 1

did you find the derivative?

Answer 2

I think is x(x-9)^1/3 I was wondering if we can go step by step

Answer 3

then I got it (1/3)x(x-9)^-2/3

Answer 4

hmm i am thinking it is
\[f(x)=x^3\sqrt{x-9}\] but maybe it is something else

Answer 5

is it
\[f(x)=x\sqrt[3]{x-9}\]?

Answer 6

yes

Answer 7

second one?

Answer 8

yes

Answer 9

ok so not x cubed but the cubed root
got it
you need the product rule for this because it is a product

Answer 10

so your derivative is wrong, looks like you just left the \(x\) there hanging about

Answer 11

\[\frac{ 1 }{ 3 }x(x-9)^{-2/3}\]

Answer 12

yeah that is part of it

Answer 13

\((fg)'=f'g+g'f\) is the product rule
you have \(x\sqrt[3]{x-9}\) so one part of the derivative is
\[\frac{1}{3}x(x-9)^{-2/3}\] but also you have at add \[\sqrt[3]{x-9}\]

Answer 14

and I think then is \[(x-9)^{1/3}\]

Answer 15

right, but now you have to set it equal to zero and solve, so you need to get it out of that exponential notation

Answer 16

I have \[\frac{ 1 }{ 3 }x(x-9)^{-2/3}+(x-9)^{1/3} but then I get lost from there..\]

Answer 17

lol add

Answer 18

what you got is
\[\frac{x}{3\sqrt[3]{x-9}}+\sqrt[3]{x-9}\] you got to add them up

Answer 19

Ahh ok..sorry this is my first time using openstudy a friend recommended it me

Answer 20

exponential notation is great for taking derivatives but not so good for solving equations

Answer 21

you are doing fine, it is going to be algebra from here on in

Answer 22

you got how to add them up, or no?

Answer 23

I think so 4x-27\[\frac{ 4x-27 }{ 3(x-9)^{2/3} }\]

Answer 24

wow ok then two steps and you are done

Answer 25

critical points are where the derivative is 0, set \(4x-27=0\) and solve, and also where the derivative is undefined, set \(x-9=0\) and solve

Answer 26

Wow thanks alot I got it now:)

Answer 27

yw but honestly you did all the work!

Answer 28

thank you:) I was wondering is this service free or do I have to pay after asking a certain amount of questions?

Answer 29

Free.

Answer 30

cool.

Answer 31

Ask away :)

But close the question after it has been satisfactorily answered and post the next question separately.

Answer 32

really? i get $10 per answer

Answer 33

$20 for correct ones

Answer 34

LQTM

Answer 35

Laughing Quietly to Myself.