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mathcalculus

  • 2 years ago

H-E-L-P Determine the extrema of below on the given interval f(x)=5x^3-61x^2+16x+3 (a) on [0,4] The minimum is ?? and the maximum is ?? (b) on [-9,9] The minimum is ?? and the maximum is ?? please solve so i can know which answer i got wrong.

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  1. wio
    • 2 years ago
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    Do you know the derivative?

  2. mathcalculus
    • 2 years ago
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    yes i did everything. x= 2/15 and x= 8

  3. mathcalculus
    • 2 years ago
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    those are the critical points.

  4. mathcalculus
    • 2 years ago
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    left end point: f(0)= 3 critical points: x= 2/15 f(2/15)= 4.06074 x=8 f(8)= -1213 Right Point: f(4)= -589

  5. wio
    • 2 years ago
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    Okay you don't consider \(f(8)\) for the \([0,4]\) interval..

  6. mathcalculus
    • 2 years ago
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    oh......

  7. wio
    • 2 years ago
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    It's apparent that \(f(2/15)\) is the maximum.

  8. wio
    • 2 years ago
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    And the minimum is going to be \(f(4)\)

  9. mathcalculus
    • 2 years ago
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    just 2/15? or do we write that the max as: 4.06074

  10. mathcalculus
    • 2 years ago
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    so the min has to be: -589

  11. wio
    • 2 years ago
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    I said \(f(2/15)\) which is equal to \(4.06074\)

  12. mathcalculus
    • 2 years ago
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    okay. then what's the minimum

  13. wio
    • 2 years ago
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    Now you just need to check 9 and -9 for the other interval.

  14. mathcalculus
    • 2 years ago
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    since i can't use f(8)

  15. wio
    • 2 years ago
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    For the \([0,4]\) interval, the minimum is -589 right?

  16. mathcalculus
    • 2 years ago
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    i think so...

  17. wio
    • 2 years ago
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    For the \([-9,9]\) interval... you can consider \(f(8)\), but you also need to consider \(f(-9)\) and \(f(9)\)

  18. mathcalculus
    • 2 years ago
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    after i do all the work, the problem is i don't know how to pick the min and max.

  19. mathcalculus
    • 2 years ago
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    for f(-9)= -8727 and for f(9) = -1149.

  20. mathcalculus
    • 2 years ago
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    Is this correct ?? (a) on [0,4] The minimum is -589 and the maximum is 4.06074 (b) on [-9,9] The minimum is -8727 and the maximum is -1149

  21. wio
    • 2 years ago
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    Yeah... the minimum is the LOWEST value the maximum is the HIGHEST value.

  22. wio
    • 2 years ago
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    You only have to consider the values at critical points and endpoints.

  23. mathcalculus
    • 2 years ago
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    i submitted this as my answer but it says its wrong. :(

  24. wio
    • 2 years ago
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    You must be doing it wrong then... somehow.

  25. mathcalculus
    • 2 years ago
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    i know that's why im asking you if the answer i had up there are correct.

  26. wio
    • 2 years ago
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    What's your derivative?

  27. mathcalculus
    • 2 years ago
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    15x^2-122x+16

  28. mathcalculus
    • 2 years ago
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    can you get back to me with answer so i can see if its correct. i dont want to go step by step if its wrong in the end. i tried this problem several times...

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