Final answer:
To find the numbers b such that the average value of /( x) = 2 6x - 3x 2 on the interval [0,b] is 3, we need to set up an equation using the average value formula. The equation can be solved using algebraic methods or graphing to find the values of b that satisfy the equation.
Step-by-step explanation:
To find the numbers b such that the average value of /( x) = 2 6x - 3x 2 on the interval [ o,b] is 3, we need to set up an equation using the average value formula. The formula is: Average = (1/b-0) ∫(0 to b) (2 6x - 3x 2) dx. We can solve this equation to find the value of b that makes the average equal to 3.
Simplifying the equation and integrating, we get: 3 = (1/b) [(6/3)x^3 - (3/2)x^2] from 0 to b. Evaluating the integral and solving for b, we get b^3 - (3/2)b^2 = 2.
This equation can be solved using algebraic methods or graphing to find the values of b that satisfy the equation.