Question

If I have a function that is bent to the right from ]-inf.;0[ and bend to the left from ]0;inf.[ but the second derivative is not defined at x=0 but I also know that there is a kink at x=0 do I than include the 0 in my intervals or do I leave the 0 out because the second derivative is not defined at x=0? If I have a function that is bent to the right from ]-inf.;0[ and bend to the left from ]0;inf.[ but the second derivative is not defined at x=0 but I also know that there is a kink at x=0 do I than include the 0 in my intervals or do I leave the 0 out because the second derivative is not defined at x=0? @Mathematics

Answer 1

I'm not sure it's possible to tell based on just that information. For example, the function \[f(x)=\sqrt{x}\] has a second derivative \[f''(x)=-\frac{1}{4x^{\frac{3}{2}}}\]. f(0) is defined, but f''(0) is not defined. The fact that there is a kink at x=0 does not mean that it's undefined, it just means the function is not continuous.

Answer 2

But If I want to describe how the function bends, do I then include the 0 in the intervals or do I leave it out?