Question

Examine if the Rolle’s theorem applies to anyone of the following functions:

f(x) = [x] for x∈[– 2, 2]

Answer 1

Given function is:

⇒ f(x) = [x] for x∈[ – 2, 2]

Let us check the continuity of the function ‘f’.

Here in the interval x∈[ – 2, 1], the function has to be Right continuous at x = 2 and left continuous at x = 2.

Right Hand Limit:

Left Hand Limit:

From (1) and (2), we can see that the limits are not the same so, the function is not continuous in the interval [– 2, 2].

∴ Rolle’s theorem is not applicable for the function f in the interval [ – 2, 2].