Find a value c in the interval [0,1] such that f(c) is equal to the average value?

f(x)=25–x^2 is the function.





I've already found what the average value of the function is: 24.66.

Find a value c in the interval [0,1] such that f(c) is equal to the average value?
f(c) = 24.66 when 25 - c^2 = 24.66.





c^2 = 0.34


and restricting c to [0, 1] means c must be the positive root.





c = 0.583.