Question

Check whether the conditions of Rolle’s theorem are satisfied by the function f(x) = x² – 4x + 3, x ∈ [1, 3].

Answer 1

The function f given as f(x) = x² – 4x + 3 is polynomial function.

Hence, it is continuous on [1, 3] and differentiable on (1, 3).

Now, f(1) = 1² – 4(1) + 3

= 1 – 4 + 3

= 0

And f(3) = 3² – 4(3) + 3

= 9 – 12 + 3

= 0

∴ f(1) = f(3)

Thus, the function f satisfies all the conditions of Rolle’s theorem.