Exercise · ZW-SMOOTH-FUNCTION-004 · ★☆☆ Basic
What class is \(f(x)=x^{5}\)?
Choose one option.
Show answer
- C. \(C^{\infty}\)
Explanation
A polynomial has derivatives of every order, and the sixth derivative of \(x^{5}\) is zero.
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
- ZW-SMOOTH-FUNCTION-001 What does it mean for f to be of class C^∞?
- ZW-SMOOTH-FUNCTION-002 Which of these functions from ℝ to ℝ is smooth?
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- ZW-SMOOTH-FUNCTION-005 Let f(x)=x|x|. What class is f?
- ZW-SMOOTH-FUNCTION-006 Let f(x)=x^2 if x≥ 0 and f(x)=0 if x<0. Is f smooth?
- 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?