Rolle-s Theorem is not applicable to f x - x - in -2-2- because-A- is not continuous in -2-2-B- LHL - RHL at x -0C- is not derivable in -2-2D- f 2 - f -2

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Relation between Continuity and Differentiability

Rolle's Theor...

Question

Rolle's Theorem is not applicable to f(x) = |x| in (-2, 2), because:

f(2) ≠ f(-2)

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is not continuous in [-2, 2]

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LHL ≠ RHL at x = 0

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is not derivable in (-2, 2)

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Solution

The correct option is D
is not derivable in (-2, 2)

(x) = | x | is continuous in [-2, 2].

Also (2) = (-2) = 2, but (x) is not derivable in (-2, 2)

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Similar questions

We can’t apply rolle’s theorem on f(x) = |x| on the interval [-2, 2] because -

Statement $1 :$ If $g (x)$ is a differentiable function, $g (2) \neq 0,$ $g (- 2) \neq 0$ and Rolle's theorem is not applicable to $f (x)$ $= \frac{x^{2} - 4}{g (x)}$ in $[- 2, 2]$ , then $g (x)$ has at least one root in $(- 2, 2)$ .
Statement $2 :$ If $f (a) = f (b)$ , then Rolle's theorem is applicable for $x \in (a, b)$

Q. Rolle's theorem is not applicable to the function f(x)=|x| defined on [-1,1] because

Q. Rolle's theorem is not applicable to the function f(x) = |x| defined on [–1, 1] because
[AISSE 1986; MP PET 1994, 95]

f is not continuous on [ –1, 1]

Q. If

f (x) = 4 - (6 - x)^{2 / 3}, i n [5, 7],

on f(x)

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Rolle's Theorem is not applicable to f(x) = |x| in (-2, 2), because:

The correct option is D is not derivable in (-2, 2) (x) = | x | is continuous in [-2, 2]. Also (2) = (-2) = 2, but (x) is not derivable in (-2, 2)

The correct option is D
is not derivable in (-2, 2)

(x) = | x | is continuous in [-2, 2].

Also (2) = (-2) = 2, but (x) is not derivable in (-2, 2)