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anonymous

  • one year ago

Anyone good at finding critical points???

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  1. anonymous
    • one year ago
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    \[y=3x^2-96\sqrt{x}\]

  2. ChillOut
    • one year ago
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    Take it's derivative y'. Do you know how?

  3. anonymous
    • one year ago
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    I know i have to take y' but that's the thing, would it be \[6x-48(x)^{-1/2}\] ??

  4. ChillOut
    • one year ago
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    Correct.

  5. anonymous
    • one year ago
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    then?

  6. anonymous
    • one year ago
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    umm

  7. anonymous
    • one year ago
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    I'm confused :(

  8. ChillOut
    • one year ago
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    Now, what does the derivative tells you about your original function?

  9. anonymous
    • one year ago
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    Don't i have to solve for the independent variable?

  10. ChillOut
    • one year ago
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    You have to solve f'(x)=0.

  11. anonymous
    • one year ago
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    yeah that's where i got stuck, because i'm used to questions where i favtor (x+y)(x+y)

  12. anonymous
    • one year ago
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    Factor*

  13. ChillOut
    • one year ago
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    Well, you just need to solve f'(x)=0 really. Those points can be extrema points

  14. anonymous
    • one year ago
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    So \[6x-48(x)^{-1/2} = 0 ?\]

  15. ChillOut
    • one year ago
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    Yes.

  16. ChillOut
    • one year ago
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    It has only one solution.

  17. anonymous
    • one year ago
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    Square the whole thing?

  18. ChillOut
    • one year ago
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    Might do. Try it

  19. ChillOut
    • one year ago
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    Well, I have to leave soon, do you want me to give you the x coordinate?

  20. anonymous
    • one year ago
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    sure

  21. ChillOut
    • one year ago
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    x=4. It shouldn't be hard to find it.

  22. anonymous
    • one year ago
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    okay i got it, thank you so much

  23. ChillOut
    • one year ago
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    Now you just plug it in the original function and find its y coordinate.

  24. anonymous
    • one year ago
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    i plug the 4 instead of x?

  25. anonymous
    • one year ago
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    nvm that was a dumb question, i got it haha thanks

  26. anonymous
    • one year ago
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    y=-30?

  27. anonymous
    • one year ago
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    -144**

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