My question is Exercise 4.17 in the image attached. The question pertains to construction of smooth cut-off function that has some special properties. It is from the book Ordinary Differential Equations with Applications by Chicone. Thanks for any help! #advancedmath#ODEs#mollification#functions

Exercise 4.17. Prove that for each r > 0 there is a Co function p : R" -> [0, 1] with the following properties: p(x) = 1 for x| r, and Idp(x) |