Which of these describes $f(x) = [x]$ at $x = 1$ ?

Continuous but not differentiableCorrect answerYour answerContinuous and differentiableCorrect answerYour answerDifferentiable but not continuousCorrect answerYour answerNeither continuous nor differentiableCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$[x]$ jumps from 0 to 1 at $x = 1$ : not continuous.
A function that is not continuous cannot be differentiable.

Worth noting

Differentiable but not continuous is impossible: differentiability forces continuity.

Concept: Testing differentiability at a point
Typical timeTypical: 60 s
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The rule this testsDifferentiability

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Which of these describes f(x)=[x]f(x) = [x]f(x)=[x] at x=1x = 1x=1?

Explanation

Which of these describes $f(x) = [x]$ at $x = 1$ ?