NDA 2024 Maths · Mathematics · Application of Derivatives · easy

Rolle's theorem cannot be applied to f(x)=|x| on [-1,1] because

Single correct option

Rolle's theorem cannot be applied to

f(x)=|x|

[-1,1]

because

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Answer: (D) $f$ is not differentiable at $x=0$

Rolle's theorem needs continuity on

[a,b]

, differentiability on

(a,b)

and

f(a)=f(b)

. Here

f

is continuous and

f(-1)=f(1)=1

, but at

x=0

the left derivative is

-1

and the right derivative is

+1

, so

f

is not differentiable on

(-1,1)

. Trap: continuity is satisfied, so the first two options are false.

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