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
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
You need to colve this cubic $\displaystyle 2b+3b^2-b^3 - 3=0$
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 $\displaystyle P(x)$ if $\displaystyle P(a)=0$ then x-a is a factor of $\displaystyle P(x)$
Example to follow is here. The Fundamental Theorem of Algebra