anonymous
  • anonymous
draw a graph of the function and indicate the average value \[f(x)=x ^{3}-5x ^{2}+10; \left[ 0,4 \right]\]
Mathematics
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anonymous
  • anonymous
draw a graph of the function and indicate the average value \[f(x)=x ^{3}-5x ^{2}+10; \left[ 0,4 \right]\]
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
average value is \[\frac{f(4)-f(0)}{4-0}\]
anonymous
  • anonymous
don't I use the anti-derivative of the function?
anonymous
  • anonymous
oh i see you want \[\frac{1}{4}\int_0^4(x^3-5x+10)dx\]

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anonymous
  • anonymous
aka "mean value" right
anonymous
  • anonymous
yes I believe that is what the question calls for
anonymous
  • anonymous
ok the "anti derivative" is not too bad because this is a polynomial it is \[\frac{x^4}{4}-\frac{5x^2}{2}+10x\]
anonymous
  • anonymous
(5x^3)/3 right
anonymous
  • anonymous
plug in 4 ignore 0 because that just gives you 0 then divide by 4
anonymous
  • anonymous
right i did all that. i got approx. -.75. does that seem correct?
anonymous
  • anonymous
it is \(-5x\) or \(-5x^2\) ?
anonymous
  • anonymous
-5x^2
anonymous
  • anonymous
oooh ok
anonymous
  • anonymous
then no it is \(-\frac{2}{3}\)
anonymous
  • anonymous
ok i get that. But how would they go on the graph. Could you give me a crude drawing?
anonymous
  • anonymous
here is a nice drawing http://www.wolframalpha.com/input/?i=x^3-5x^2%2B10+domain+0..4
anonymous
  • anonymous
and the average value represented on the graph would just be a straight line at -2/3?
anonymous
  • anonymous
that i do not know sorry
anonymous
  • anonymous
ok thank you

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