If the function f(x) = x3 – 6x2 + ax + b is defined on [1, 3] satisfies the hypothesis of Rolle’* theorem, then find the values of a and b.
Given f(x) = x3 – 6x2 + ax + b
f(1) = f(3)
⇒ 1 – 6 + a + b = 27 – 54 + 3a + b
⇒ a + b – 5 = 3a + b – 27
⇒ 2a = 22
⇒ a = 11, b ∈ R
