1. The problem statement, all variables and given/known data define a function f:R->R is given by f(x)=(|x|^a)*(sin(1/x)) if x is not equal 0 , and f(x)=0 if x=o . and a>0. for which values of a is f differentiable at x=o 2. The attempt at a solution obviously, a=2 is one of the solution , but how about other values? can someone can show me the prove for other value of a that this function is differentiable at x=0?