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anonymous

  • 2 years ago

draw a graph of the function and indicate the average value \[f(x)=x ^{3}-5x ^{2}+10; \left[ 0,4 \right]\]

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  1. anonymous
    • 2 years ago
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    average value is \[\frac{f(4)-f(0)}{4-0}\]

  2. anonymous
    • 2 years ago
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    don't I use the anti-derivative of the function?

  3. anonymous
    • 2 years ago
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    oh i see you want \[\frac{1}{4}\int_0^4(x^3-5x+10)dx\]

  4. anonymous
    • 2 years ago
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    aka "mean value" right

  5. anonymous
    • 2 years ago
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    yes I believe that is what the question calls for

  6. anonymous
    • 2 years ago
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    ok the "anti derivative" is not too bad because this is a polynomial it is \[\frac{x^4}{4}-\frac{5x^2}{2}+10x\]

  7. anonymous
    • 2 years ago
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    (5x^3)/3 right

  8. anonymous
    • 2 years ago
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    plug in 4 ignore 0 because that just gives you 0 then divide by 4

  9. anonymous
    • 2 years ago
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    right i did all that. i got approx. -.75. does that seem correct?

  10. anonymous
    • 2 years ago
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    it is \(-5x\) or \(-5x^2\) ?

  11. anonymous
    • 2 years ago
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    -5x^2

  12. anonymous
    • 2 years ago
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    oooh ok

  13. anonymous
    • 2 years ago
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    then no it is \(-\frac{2}{3}\)

  14. anonymous
    • 2 years ago
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    ok i get that. But how would they go on the graph. Could you give me a crude drawing?

  15. anonymous
    • 2 years ago
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    here is a nice drawing http://www.wolframalpha.com/input/?i=x^3-5x^2%2B10+domain+0..4

  16. anonymous
    • 2 years ago
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    and the average value represented on the graph would just be a straight line at -2/3?

  17. anonymous
    • 2 years ago
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    that i do not know sorry

  18. anonymous
    • 2 years ago
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    ok thank you

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spraguer (Moderator)
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