Question of the Day
Where does Rolle's theorem hold for f(x) = x² − 4x + 3 on [1, 3]?
f(x) = x² − 4x + 3 is continuous on [1, 3], differentiable on (1, 3) and f(1) = f(3) = 0. Find the point c in (1, 3) given by Rolle's theorem.
Solution
f′(x) = 2x − 4. Setting f′(c) = 0 gives c = 2, which lies in (1, 3). So Rolle's theorem holds at c = 2.