Find the number b such that the average value of f(x)=2+6x-3x^2 on the intervak [0, b] is equal to 3.

so I did the integal from 0 to b of 2+6x-3x^2 which is 2x+3x^2-x^3

now what? Do i set it equal to 3 and find out what b is?

Thanks

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- July 28th 2010, 05:38 PMsoftballchickAverage value of a function.
Find the number b such that the average value of f(x)=2+6x-3x^2 on the intervak [0, b] is equal to 3.

so I did the integal from 0 to b of 2+6x-3x^2 which is 2x+3x^2-x^3

now what? Do i set it equal to 3 and find out what b is?

Thanks - July 28th 2010, 05:42 PMAlso sprach Zarathustra
when

You looking for b when f(c)=3. - July 28th 2010, 05:45 PMpickslides
For find

- July 28th 2010, 06:15 PMsoftballchick
right, so I set 2x+3x^2-x^3 = 3 right?

= x(2+3x-x^2)

=x(x -1) (x-2)

ahhh i'm confused.... - July 28th 2010, 06:20 PMpickslides
- July 28th 2010, 06:28 PMsoftballchick
um... I don't think I do. could u elaborate more? Thanks

- July 28th 2010, 06:44 PMpickslides
You need to colve this cubic

To do that you should employ the factor theorem. It's really not something that can be explained very well in a few lines but here goes.

The Factor Theorem: For the polynomial if then x-a is a factor of

Example to follow is here. The Fundamental Theorem of Algebra - July 28th 2010, 06:58 PMAlso sprach Zarathustra
Mr. pickslides I convinced you aware that the roots not so "nice"...

- July 28th 2010, 07:06 PMpickslides