A community for students.
Here's the question you clicked on:
 0 viewing
eroshea
 2 years ago
find all the critical point of f(x) = 3x^(5/3)  15x^(2/3)
eroshea
 2 years ago
find all the critical point of f(x) = 3x^(5/3)  15x^(2/3)

This Question is Closed

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Critical points are points where the derivative is zero.

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Of course, differentiate first :)

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1let's see.... \[\Large \frac{d}{dx}\left(3x^{\frac53}15x^{\frac23}\right)=5x^{\frac23}10x^{\frac13}\]

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Try 0. the derivative doesn't exist, because you have... \[\Large 5x^{\frac23}10x^{\frac13}=5x^{\frac23}\frac1{10x^{\frac13}}\] an x in the denmoinator.

eroshea
 2 years ago
Best ResponseYou've already chosen the best response.1so that will be disregarded right? so i will have 2 for the value of x

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1so yes, that is a critical point (sorry, I forgot to mention that points where the derivative does not exist are also critical points)

eroshea
 2 years ago
Best ResponseYou've already chosen the best response.1so what next? how will i graph?

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Hang on, I'm not sure about the 2 yet. Let's try equating the derivative to zero. \[\Large0=5x^{\frac23}\frac1{10x^{\frac13}}\]\[\Large5x^{\frac23}=\frac1{10x^{\frac13}}\]\[\Large5x^{\frac23}\cdot 10x^{\frac13}=1\]\[\Large50x=1\] Are you sure it's x = 2? :P

eroshea
 2 years ago
Best ResponseYou've already chosen the best response.1can you factor out 5x^(1/3) from 5x^(2/3)−10x^(−1/3)?

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1You can... but why would you do that?

eroshea
 2 years ago
Best ResponseYou've already chosen the best response.1what will be the answer if you would factor out that one? 5x^(1/3) i got a little confused

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1I think it leads nowhere :)

eroshea
 2 years ago
Best ResponseYou've already chosen the best response.1owh.. lol.. so x = 1/50?

eroshea
 2 years ago
Best ResponseYou've already chosen the best response.1what is the answer if i would take out 5x^(1/3) from 5x^(2/3) i really am confused on what will be the outcome

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Hang on, I may have made a mistake.

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Okay... apparently, 2 was right.

eroshea
 2 years ago
Best ResponseYou've already chosen the best response.1yehey :D so.. what to do next ?

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1just like that? You're not going to ask me where my error was? :/ You didn't spot it yet... means you may well commit the same... come on, a little challenge :P

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1\[\Large0=5x^{\frac23}\frac1{10x^{\frac13}}\] I should not have put 10 in the denominator. Big mistake. Correct would be \[\Large0=5x^{\frac23}\frac{10}{x^{\frac13}}\color{green}\checkmark \]

eroshea
 2 years ago
Best ResponseYou've already chosen the best response.1you shouldn't include 10 in the denominator.. it should be on the numerator :D

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1yeah that :) sorry about that. I might be getting drowsy.

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1And as far as I know... we're done.

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1We already have the critical points.

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1whoops... you'll need to consult one of the big guys for that :3 I'm rather terrible at graphing, you see...

eroshea
 2 years ago
Best ResponseYou've already chosen the best response.1owh.. that'll be okay then.. thanks for the help! :D
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.