Class 12

Math

Calculus

Continuity and Differentiability

Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example?

(i) $f(x)=[x]$ for $x∈[5,9]$

(ii) $f(x)=[x]$ for $x∈[−2,2]$

(iii) $f(x)=x_{2}−1$ for $x∈[1,2]$