Find the numbers b such that the average value of f(x) = 8 + 10x − 9x^2 on the interval [0, b] is equal to 9.

Question

Find the numbers b such that the average value of f(x) = 8 + 10x − 9x²  on the interval [0, b] is equal to 9.

Answer 1

I was trying to keep this video under five minutes, so after you find the values:

b = (5 ± √(13))/6

you split them up into different fractions

b = (5 + √(13))/6

b = (5 - √(13))/6

and make sure they are both greater than 0 since the left endpoint is 0.