If x-x-2- then at x-2- fx is

The correct option is B Continous but not differentiable f'(x) = 1 at x lt; 2 f'(x) = 1 at x gt; 2 Therefore, not differentiable But is continous as ...

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Standard XII

Mathematics

Continuity of Composite Functions

If x=|x-2|, t...

Question

If f(x) = |x - 2|, then at x = 2, f'(x) is

Continous but not differentiable

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Continous and differentiable both

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Neither continous nor differentiable

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Differentiable but not continous

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Solution

The correct option is A
Continous but not differentiable

f'(x) = -1 at x < 2

f'(x) = 1 at x > 2

Therefore, not differentiable

But is continous as it is composition of two functions i.e., polynomial and modulus

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(correct answer + 1, wrong answer - 0.25)

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If f(x) = |x - 2|, then at x = 2, f'(x) is

The correct option is A Continous but not differentiable f'(x) = -1 at x < 2 f'(x) = 1 at x > 2 Therefore, not differentiable But is continous as it is composition of two functions i.e., polynomial and modulus

The correct option is A
Continous but not differentiable

f'(x) = -1 at x < 2

f'(x) = 1 at x > 2

Therefore, not differentiable

But is continous as it is composition of two functions i.e., polynomial and modulus