Exercise · ZW-SMOOTH-FUNCTION-005 · ★★☆ Intermediate
Let \(f(x)=x|x|\). What class is \(f\)?
Choose one option.
Show answer
- B. \(C^{1}\) but not \(C^{2}\)
Explanation
Since \(f'(x)=2|x|\) is continuous but \(f''(x)=2\,\mathrm{sgn}(x)\) jumps at \(0\), \(f\) is \(C^{1}\) but not \(C^{2}\).
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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- ZW-SMOOTH-FUNCTION-007 If f and g from ℝ to ℝ are smooth, what can be said about g∘ f?
- ZW-SMOOTH-FUNCTION-008 Let f(x)=x^2sin (1/x) for xne 0 and f(0)=0. Which statement is correct?
- ZW-SMOOTH-FUNCTION-009 What is a diffeomorphism between two smooth manifolds?