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anonymous
 3 years ago
find all the critical point of f(x) = 3x^(5/3)  15x^(2/3)
anonymous
 3 years ago
find all the critical point of f(x) = 3x^(5/3)  15x^(2/3)

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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0is my answer correct?

terenzreignz
 3 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so that will be disregarded right? so i will have 2 for the value of x

terenzreignz
 3 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)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so what next? how will i graph?

terenzreignz
 3 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0can you factor out 5x^(1/3) from 5x^(2/3)−10x^(−1/3)?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0what will be the answer if you would factor out that one? 5x^(1/3) i got a little confused

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0owh.. lol.. so x = 1/50?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0what 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
 3 years ago
Best ResponseYou've already chosen the best response.1Hang on, I may have made a mistake.

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yehey :D so.. what to do next ?

terenzreignz
 3 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
 3 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 \[\Large0=5x^{\frac23}\frac{10}{x^{\frac13}}\color{green}\checkmark \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you shouldn't include 10 in the denominator.. it should be on the numerator :D

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

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

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

terenzreignz
 3 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...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0owh.. that'll be okay then.. thanks for the help! :D
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