How do you show that the function "f(x) = {[x-1;x<2], [2x-3;x>=2]}" is not differentiable at "x=2”?

Expert Solution

For a function to be differentiable at a point,it must be continuous at that point (have the same value as you approach from the left as when you approach from the right). it must also have the same derivative (slope) as you approach the x-value from the left as when you approach the x- value from the right.

So, let’s see. As we approach 2 from the left, we are using the function f(x)=x - 1, so its y-value will be 1. As we approach from the right, we are using the function f(x)=2x–3, so the y-value will be 1. So, no problem with continuity.

no limit exist.

Sankar Maity answered 2 years ago

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