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

Question

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

aka "mean value" right

anonymous · Answer

yes I believe that is what the question calls for

anonymous · Answer

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 · Answer

(5x^3)/3 right

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

-5x^2

anonymous · Answer

oooh ok

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

anonymous · Answer

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

anonymous · Answer

that i do not know
sorry

anonymous · Answer

ok thank you