MATTW20
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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anonymous
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average value is
\[\frac{f(4)f(0)}{40}\]

MATTW20
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don't I use the antiderivative of the function?

anonymous
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oh i see you want
\[\frac{1}{4}\int_0^4(x^35x+10)dx\]

anonymous
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aka "mean value" right

MATTW20
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yes I believe that is what the question calls for

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

MATTW20
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(5x^3)/3 right

anonymous
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plug in 4
ignore 0 because that just gives you 0
then divide by 4

MATTW20
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right i did all that. i got approx. .75. does that seem correct?

anonymous
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it is \(5x\) or \(5x^2\) ?

MATTW20
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5x^2

anonymous
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oooh ok

anonymous
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then no it is \(\frac{2}{3}\)

MATTW20
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ok i get that. But how would they go on the graph. Could you give me a crude drawing?


MATTW20
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and the average value represented on the graph would just be a straight line at 2/3?

anonymous
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that i do not know
sorry

MATTW20
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ok thank you