Question

Find the numbers b such that the average value of f(x) = 15x2 − 42x + 6 on the interval [0, b] is equal to 2.

Answer 1

The average value (a) of f(x) on the interval [0, b] is given by

`a= (1)/(b) \int\limits^b_0 {(15x^(2)-42x+6)} \, dx = 5b^(2) -21b +6`
You want this value equal to 2, so you have

`5b^(2) -21b +6 = 2`

`(5b-1)(b-4)=0`

The values of b are 0.2 and 4.