Posted by **li** on Saturday, December 3, 2011 at 4:06pm.

Find the average value of the function

f(x)=8x^2-5x+6 , on the interval [3,5]. Find the value of x-coordinate at which the function assumes it's average value.

what is the average value = to ?

what is the x coordinate = to ?

Thanks

- calculus -
**MathMate**, Sunday, December 4, 2011 at 1:02pm
Let f(x)=8x^2-5x+6

The average value is the definite integral divided by the interval.

I=∫f(x)dx

=∫(8x^2-5x+6)dx

=[(8/3)x^3-(5/2)x^2+6x] from 3 to 5

=700/3

Average value, a

= I/(5-3)

= 350/3

To find x where f(x)=a, solve for x in

f(x) = 8x^2-5x+6 = 350/3

However, out of the two solutions, x=-3.42 and x=4.045, you will report the solution which is within the interval [3,5] and reject all solutions outside of the interval.

## Answer This Question

## Related Questions

- Calculus - Find the average value of the function f(x) 8x^2-9x+8 on the interval...
- Calculus - Find the average value of the function over [1,3] and all values of x...
- Calculus - I'm supposed to find the average value of the function over the given...
- calculus - Consider the function f(x)=–3x3–1x2+1x+1Find the average slope of ...
- Calculus - a)Find the average value of f(x) = e-x over the interval [0,k] b)What...
- Calculus Please help! - f(x) -2x^3+2x^2-3x+2 Find the average slope of this ...
- Calculus AB - The average value of a continuous function f(x) on the closed ...
- calculus - Consider the given function and the given interval. f(x) = 4 sin x &#...
- Calculus - Find the average value of the function f(x)= 8/ (3+x)^2 on the ...
- Calculus - Find the average value of the function f(x)= 8/ (3+x)^2 on the ...

More Related Questions