Question

Rolle's theorem is not applicable for the function $f\left(x\right)=|x|$ in the interval $[-1,1]$ because:

• A. $f^{\prime }\left(1\right)$ does not exist
• B. $f^{\prime }(-1)$ does not exist
• C. $f\left(x\right)$ is discontinuous at $x=0$
• D. $f^{\prime }\left(0\right)$ does not exist

Answer 1

Answer: (D)

$f^{\prime }\left(0\right)$ does not exist

Rolle's theorem is applicable only if function is continuous and differentiable

But $f\left(x\right)=|x|$ is not differentiable at $x=0$, i.e. $f^{\prime }\left(0\right)$ does not exist