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Q)

True or False: Rolle's theorem is applicable for the function $f(x)=|x-1|$ in [0,2].

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A)
Toolbox:
  • Rolle's Theorem :Let $f$ be a real valued function defined once close interval $[a,b]$,such that
  • $\quad(i)$ it is continuous on the closed interval $[a,b]$.
  • $\quad(ii)$ it is differentiable in the open interval $(a,b)$.
  • $\quad(iii)$ $f(a)=f(b)$,then there exists a real numbers $c\in (a,b)$ such that $f'(c)=0$
Let $f(x)=\mid x-1\mid$
The given interval is $[0,2]$.
Consider when $x=1$
$f(x)=0$
Which is not differentiable.
Hence Rolle's theorem is not verified.
Hence it is a False statement.
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