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Prove that the greatest integer function...

Prove that the greatest integer function defined by `f(x) = [x], 0 < x < 3` is not differentiable at `x = 1 and x = 2`.

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To prove that the greatest integer function defined by \( f(x) = [x] \) (where \([x]\) is the greatest integer less than or equal to \(x\)) is not differentiable at \( x = 1 \) and \( x = 2 \), we will check the continuity of the function at these points. ### Step 1: Check Continuity at \( x = 1 \) To check the continuity of \( f(x) \) at \( x = 1 \), we need to evaluate the following: 1. \( f(1) \) 2. The right-hand limit \( f(1^+) \) ...
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