Finding b such that average value of 1+10x-3x² on [0,b] equals 4

[credd741]

i have a question
how would you find a number b such that the average value of
f(x)= 1+10x-3x^2 on the interval [0,b] is equal to 4.

i have tried to set this equal to 4 but everytime i try to solve for b i get some number but it is always wrong. please help!

 

[berkeman]

Welcome to the PF. How do you calculate the average of a function over an interval? What is the relevant equation?

 

[credd741]

the relevant equation is the f(x)=1+10x-3x^2

 

[dontdisturbmycircles]

In order to find the average value of a function over a specified interval [0,b] you must integrate the function on that interval and divide by the interval length.

Can you formulate an equation which states these facts in terms of b and solve for b?