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

1. anonymous

average value is $\frac{f(4)-f(0)}{4-0}$

2. anonymous

don't I use the anti-derivative of the function?

3. anonymous

oh i see you want $\frac{1}{4}\int_0^4(x^3-5x+10)dx$

4. anonymous

aka "mean value" right

5. anonymous

yes I believe that is what the question calls for

6. anonymous

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

7. anonymous

(5x^3)/3 right

8. anonymous

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

9. anonymous

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

10. anonymous

it is $$-5x$$ or $$-5x^2$$ ?

11. anonymous

-5x^2

12. anonymous

oooh ok

13. anonymous

then no it is $$-\frac{2}{3}$$

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

that i do not know sorry

18. anonymous

ok thank you