Find the numbers b such that the average value of f(x) = 3 + 10x − 6x2 on the interval [0, b] is equal to 4.

Question

b =  ________(smaller value)

b = ________ (larger value)

Answer 1

A(b) = (1/b) ∫₀^b[ 3 +10x −6x²]dx

A(b) = (1/b) [ 3b +5b² −2b3]

A(b)= 3 +5b −2b²

4 = 3 +5b −2b²

-1 +5b −2b² =0

b= ( 5 +√17 ) / 4

b= ( 5 −√17 ) / 4