Assertion (A): $f(x) = [x]$ is not differentiable at $x = 2$ .
Reason (R): $f(x) = [x]$ is not continuous at $x = 2$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

R is true: $[x]$ jumps from 1 to 2 at $x = 2$ .
A is true, and R is the reason: a function that is not continuous cannot be differentiable.

Concept: Discontinuity rules out differentiability
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The rule this testsDifferentiability

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Assertion (A): f(x)=[x]f(x) = [x]f(x)=[x] is not differentiable at x=2x = 2x=2.Reason (R): f(x)=[x]f(x) = [x]f(x)=[x] is not continuous at x=2x = 2x=2.

Explanation

Assertion (A): $f(x) = [x]$ is not differentiable at $x = 2$ .
Reason (R): $f(x) = [x]$ is not continuous at $x = 2$ .