Q65 / 125 · BITSAT 2017 · Mathematics

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

A
$f^{'} (1)$ does not exist
B
$f^{'} (- 1)$ does not exist
C
$f (x)$ is discontinuous at $x = 0$
Correct answer
D
$f^{'} (0)$ does not exist

Solution

We have,

$f (x) = | x |$

We know that the function is not differentiable at the sharp edges. Hence, $f (x)$ is not differentiable at $x = 0$ . Therefore, Rolle's theorem is not applicable for the function

$f (x) = | x |$ in $[- 1, 1]$

$∵ f^{'} (0)$ does not exist.

Hence, the correct answer is option: 'D'.

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

Solution

More Application of Derivatives Questions

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