- #1
15adhami
- 6
- 0
Hello,
Me and my friend were talking about differentiability of some piece-wise functions, but we thought of a problem that we could were not able to come to an agreement on. If the function is:
y=sin(x) for x≠0
and
y=x^2 for x=0,
Is this function differentiable? The graph looks like a normal sin graph, but the derivative at x=0 is 0, although on the graph it looks like 1. I thought that because y=x^2 at only 1 point, you cannot get the derivative at x=0 because there wouldn't be a dx or a dy, as there is no change in the function. So I thought that it would default to the derivative of sin(x), making the whole function differentiable. My friend thought that it is not differentiable. What is the correct answer? Thank you.
Me and my friend were talking about differentiability of some piece-wise functions, but we thought of a problem that we could were not able to come to an agreement on. If the function is:
y=sin(x) for x≠0
and
y=x^2 for x=0,
Is this function differentiable? The graph looks like a normal sin graph, but the derivative at x=0 is 0, although on the graph it looks like 1. I thought that because y=x^2 at only 1 point, you cannot get the derivative at x=0 because there wouldn't be a dx or a dy, as there is no change in the function. So I thought that it would default to the derivative of sin(x), making the whole function differentiable. My friend thought that it is not differentiable. What is the correct answer? Thank you.