Discuss the applicability of Rolle’s theorem for the following functions on the indicated intervals :

Question

Philoid · Accepted Answer

Given function is:

⇒

Let’s check the continuity at x = 1 as the equation of function changes.

Left – Hand Limit:

⇒

⇒ ......(1)

Right – Hand Limit:

⇒

⇒ ......(2)

From (1) and (2), we can see that the values of both side limits are not equal. So, the function ‘f’ is not continuous at x = 1.

∴ Rolle’s theorem is not applicable to the function ‘f’ in the interval [0,2].