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

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satellite73Best ResponseYou've already chosen the best response.1
average value is \[\frac{f(4)f(0)}{40}\]
 7 months ago

MATTW20Best ResponseYou've already chosen the best response.0
don't I use the antiderivative of the function?
 7 months ago

satellite73Best ResponseYou've already chosen the best response.1
oh i see you want \[\frac{1}{4}\int_0^4(x^35x+10)dx\]
 7 months ago

satellite73Best ResponseYou've already chosen the best response.1
aka "mean value" right
 7 months ago

MATTW20Best ResponseYou've already chosen the best response.0
yes I believe that is what the question calls for
 7 months ago

satellite73Best ResponseYou've already chosen the best response.1
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 months ago

satellite73Best ResponseYou've already chosen the best response.1
plug in 4 ignore 0 because that just gives you 0 then divide by 4
 7 months ago

MATTW20Best ResponseYou've already chosen the best response.0
right i did all that. i got approx. .75. does that seem correct?
 7 months ago

satellite73Best ResponseYou've already chosen the best response.1
it is \(5x\) or \(5x^2\) ?
 7 months ago

satellite73Best ResponseYou've already chosen the best response.1
then no it is \(\frac{2}{3}\)
 7 months ago

MATTW20Best ResponseYou've already chosen the best response.0
ok i get that. But how would they go on the graph. Could you give me a crude drawing?
 7 months ago

satellite73Best ResponseYou've already chosen the best response.1
here is a nice drawing http://www.wolframalpha.com/input/?i=x^35x^2%2B10+domain+0..4
 7 months ago

MATTW20Best ResponseYou've already chosen the best response.0
and the average value represented on the graph would just be a straight line at 2/3?
 7 months ago

satellite73Best ResponseYou've already chosen the best response.1
that i do not know sorry
 7 months ago
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