eroshea
find all the critical point of f(x) = 3x^(5/3) - 15x^(2/3)
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terenzreignz
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Critical points are points where the derivative is zero.
terenzreignz
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Of course, differentiate first :)
eroshea
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ok.. i got x=0, x=2
terenzreignz
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let's see....
\[\Large \frac{d}{dx}\left(3x^{\frac53}-15x^{\frac23}\right)=5x^{\frac23}-10x^{-\frac13}\]
eroshea
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is my answer correct?
terenzreignz
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Try 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
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so that will be disregarded right? so i will have 2 for the value of x
terenzreignz
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so yes, that is a critical point (sorry, I forgot to mention that points where the derivative does not exist are also critical points)
eroshea
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owh.. i see
eroshea
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so what next? how will i graph?
terenzreignz
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Hang 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
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can you factor out 5x^(1/3) from 5x^(2/3)−10x^(−1/3)?
terenzreignz
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You can... but why would you do that?
eroshea
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what will be the answer if you would factor out that one? 5x^(-1/3)
i got a little confused
terenzreignz
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I think it leads nowhere :)
eroshea
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owh.. lol.. so x = 1/50?
terenzreignz
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yeah :)
eroshea
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what 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
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Hang on, I may have made a mistake.
terenzreignz
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Okay... apparently, 2 was right.
terenzreignz
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sorry.
eroshea
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yehey :D
so.. what to do next ?
terenzreignz
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just 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
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\[\Large0=5x^{\frac23}-\frac1{10x^{\frac13}}\]
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
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you shouldn't include 10 in the denominator.. it should be on the numerator :D
terenzreignz
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yeah that :)
sorry about that.
I might be getting drowsy.
terenzreignz
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And as far as I know... we're done.
eroshea
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that's ok.. :))
terenzreignz
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We already have the critical points.
eroshea
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then how to graph?
terenzreignz
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whoops... you'll need to consult one of the big guys for that :3
I'm rather terrible at graphing, you see...
eroshea
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owh.. that'll be okay then.. thanks for the help! :D
terenzreignz
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No problem :)