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mathcalculus

  • 2 years ago

Help (Attached below) Determine the extrema of below on the given interval

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  1. mathcalculus
    • 2 years ago
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  2. mathcalculus
    • 2 years ago
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    i know we have to find the derivative and set it to zero

  3. mathcalculus
    • 2 years ago
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    i got x= 8 and x= 2/9

  4. mathcalculus
    • 2 years ago
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    now to have the intervals, im a little lost on...

  5. mathcalculus
    • 2 years ago
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    would there only be 2 intervals?

  6. mathcalculus
    • 2 years ago
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    or 3? 0-2/9 then 2/9-8 and 8-infinity?

  7. campbell_st
    • 2 years ago
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    ok... so whats the derivative...?

  8. mathcalculus
    • 2 years ago
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    9x^2-74x+16

  9. mathcalculus
    • 2 years ago
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    then i set it to = 0

  10. campbell_st
    • 2 years ago
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    ok... so what are the solutions...?

  11. mathcalculus
    • 2 years ago
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    x=8 and x=2/9

  12. mathcalculus
    • 2 years ago
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    critical numbers

  13. campbell_st
    • 2 years ago
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    yep... so on [0, 4] substitute x = 0, 2/9 and 4 into the original equation and find the corresponding values...

  14. mathcalculus
    • 2 years ago
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    why 4?

  15. mathcalculus
    • 2 years ago
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    thanks

  16. mathcalculus
    • 2 years ago
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    isn't 4 a y?

  17. mathcalculus
    • 2 years ago
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    and what 8?

  18. mathcalculus
    • 2 years ago
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    because the 2 critical numbers are 8 and 2/9

  19. campbell_st
    • 2 years ago
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    well (a) is asking for the location of that min and max on the interval x = 0 to x = 4 and as x = 2/9 is a critical point...you don't know its nature

  20. mathcalculus
    • 2 years ago
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    ooooooh, 8 would be the other one

  21. mathcalculus
    • 2 years ago
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    let me try it

  22. campbell_st
    • 2 years ago
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    so the value x =0 is f(0) = 2 x = 2/9 f(2/9) = 3.76 x = 4 f(4) = ?

  23. mathcalculus
    • 2 years ago
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    -334

  24. mathcalculus
    • 2 years ago
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    so the max is 3.76 and min is -334?

  25. campbell_st
    • 2 years ago
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    thats correct...

  26. campbell_st
    • 2 years ago
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    so just test x = -9, x = 8 and x = 9... and see what happens... I think x = 2/9 remains the max

  27. campbell_st
    • 2 years ago
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    its an add interval since x = -9 gives a very large negative number

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