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eroshea
 one year ago
find all the critical point of f(x) = 3x^(5/3)  15x^(2/3)
eroshea
 one year ago
find all the critical point of f(x) = 3x^(5/3)  15x^(2/3)

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

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

terenzreignz
 one year 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
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1so what next? how will i graph?

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

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

eroshea
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1I think it leads nowhere :)

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

eroshea
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1Hang on, I may have made a mistake.

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

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

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

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

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

terenzreignz
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1owh.. that'll be okay then.. thanks for the help! :D
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