Question 1184358: Verify that the obtained function is smooth at all points in your domain:
f(x)={ 2 , if 0≤x≤2.72
-----{ln(x^2),if 2.72< x < 20
-------{ x-14 , if 20≤x≤25
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website!
No, your function is not smooth in the domain [0, 25]. In fact, it's not even continuous.
What makes it continuous is the following definition:
 .
But even with the correct definition it still is not smooth, as the function is not differentiable at  and 
At , the left-hand derivative is  , while the right-hand derivative is  , so the derivative at  does not exist.
At , the left-hand derivative is  , while the right-hand derivative is  , so the derivative at  does not exist.
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