Exercise · ZW-SMOOTH-FUNCTION-006 · ★★☆ Intermediate
Let \(f(x)=x^{2}\) if \(x\ge 0\) and \(f(x)=0\) if \(x<0\). Is \(f\) smooth?
Choose one option.
Show answer
- A. It is \(C^{1}\) but not \(C^{2}\)
Explanation
\(f\) is continuous and \(f'\) exists everywhere, but \(f''\) jumps at \(0\) (from 0 to 2).
Review the concept: Smooth function
A smooth function is a function between spaces with differentiable structure that, written in local coordinates, has derivatives of all orders.
\[f\in C^{\infty}(M,N)\]
More practice problems: smooth function
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