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anonymous

  • 5 years ago

Find the intervals in which the function is increasing and decreasing. Also, find and classify all the critical points of the function using the First Derivative Test. A(t)=t^5-5t^4+20t^3-17 I am having trouble setting the derivative equal to zero. Please help!

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  1. amistre64
    • 5 years ago
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    increaseing or decreasing is a 2nd derivative test... not a 1st derivative test :)

  2. anonymous
    • 5 years ago
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    No...don't think so

  3. amistre64
    • 5 years ago
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    A' = 5t^4 -20t^3 +60t^2 A' = 5t^2(t^2 -4t +12) = 0

  4. amistre64
    • 5 years ago
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    12..6.2 (t-6) (t+2) t = 6, -2, and 0 are your crits

  5. amistre64
    • 5 years ago
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    what were you having issues with?

  6. amistre64
    • 5 years ago
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    slope is a function of the 1st derivative; concavity is a function of the 2nd derivative

  7. anonymous
    • 5 years ago
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    6 x -2 is -12, not +12

  8. amistre64
    • 5 years ago
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    hmmm.... you might be right :)

  9. amistre64
    • 5 years ago
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    my eyes were deceiving me... ;)

  10. amistre64
    • 5 years ago
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    if its got imaginary roots, then we probably dont need to both with it.... right? sqrt(16 - 48) = sqrt(-32) no "real" roots for this, go with t=0 as the critical, and it probably an inflection point

  11. anonymous
    • 5 years ago
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    Right. Thanks!

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