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MATTW20
 2 years ago
draw a graph of the function and indicate the average value
\[f(x)=x ^{3}5x ^{2}+10; \left[ 0,4 \right]\]
MATTW20
 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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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1average value is \[\frac{f(4)f(0)}{40}\]

MATTW20
 2 years ago
Best ResponseYou've already chosen the best response.0don't I use the antiderivative of the function?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1oh i see you want \[\frac{1}{4}\int_0^4(x^35x+10)dx\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1aka "mean value" right

MATTW20
 2 years ago
Best ResponseYou've already chosen the best response.0yes I believe that is what the question calls for

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1ok the "anti derivative" is not too bad because this is a polynomial it is \[\frac{x^4}{4}\frac{5x^2}{2}+10x\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1plug in 4 ignore 0 because that just gives you 0 then divide by 4

MATTW20
 2 years ago
Best ResponseYou've already chosen the best response.0right i did all that. i got approx. .75. does that seem correct?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1it is \(5x\) or \(5x^2\) ?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1then no it is \(\frac{2}{3}\)

MATTW20
 2 years ago
Best ResponseYou've already chosen the best response.0ok i get that. But how would they go on the graph. Could you give me a crude drawing?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1here is a nice drawing http://www.wolframalpha.com/input/?i=x^35x^2%2B10+domain+0..4

MATTW20
 2 years ago
Best ResponseYou've already chosen the best response.0and the average value represented on the graph would just be a straight line at 2/3?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1that i do not know sorry
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