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

1. terenzreignz Group Title

Critical points are points where the derivative is zero.

2. terenzreignz Group Title

Of course, differentiate first :)

3. eroshea Group Title

ok.. i got x=0, x=2

4. terenzreignz Group Title

let's see.... $\Large \frac{d}{dx}\left(3x^{\frac53}-15x^{\frac23}\right)=5x^{\frac23}-10x^{-\frac13}$

5. eroshea Group Title

6. terenzreignz Group Title

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.

7. eroshea Group Title

so that will be disregarded right? so i will have 2 for the value of x

8. terenzreignz Group Title

so yes, that is a critical point (sorry, I forgot to mention that points where the derivative does not exist are also critical points)

9. eroshea Group Title

owh.. i see

10. eroshea Group Title

so what next? how will i graph?

11. terenzreignz Group Title

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

12. eroshea Group Title

can you factor out 5x^(1/3) from 5x^(2/3)−10x^(−1/3)?

13. terenzreignz Group Title

You can... but why would you do that?

14. eroshea Group Title

what will be the answer if you would factor out that one? 5x^(-1/3) i got a little confused

15. terenzreignz Group Title

I think it leads nowhere :)

16. eroshea Group Title

owh.. lol.. so x = 1/50?

17. terenzreignz Group Title

yeah :)

18. eroshea Group Title

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

19. terenzreignz Group Title

Hang on, I may have made a mistake.

20. terenzreignz Group Title

Okay... apparently, 2 was right.

21. terenzreignz Group Title

sorry.

22. eroshea Group Title

yehey :D so.. what to do next ?

23. terenzreignz Group Title

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

24. terenzreignz Group Title

$\Large0=5x^{\frac23}-\frac1{10x^{\frac13}}$ I should not have put 10 in the denominator. Big mistake. Correct would be $\Large0=5x^{\frac23}-\frac{10}{x^{\frac13}}\color{green}\checkmark$

25. eroshea Group Title

you shouldn't include 10 in the denominator.. it should be on the numerator :D

26. terenzreignz Group Title

yeah that :) sorry about that. I might be getting drowsy.

27. terenzreignz Group Title

And as far as I know... we're done.

28. eroshea Group Title

that's ok.. :))

29. terenzreignz Group Title

We already have the critical points.

30. eroshea Group Title

then how to graph?

31. terenzreignz Group Title

whoops... you'll need to consult one of the big guys for that :3 I'm rather terrible at graphing, you see...

32. eroshea Group Title

owh.. that'll be okay then.. thanks for the help! :D

33. terenzreignz Group Title

No problem :)