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

Question

the average value of f(x)=25-x² on the interval [0,1] is 74/3

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

Answer 1

74 / 3 = 25 - c²

-1 / 3 = - c²

1 / 3 = c²

±√3 / 3 = c