Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Enter your answers as a comma-separated list.)
f(x) = x^9, [0, 9]
f(0) = 0
f(9) = 9^9 (wow!)
(f(9)-f(0))/9 = 9^8
f'(x) = 9x^8
so, you want c such that
f'(c) = 9^8
9c^8 = 9^8
c^8 = 9^7
c = 9^(7/8) ≈ 6.84 ∊ [0,9]