I'm new here, and wanted to ask this about a week ago, but I got the other 6 problems that I was going to ask for on my own, and with friends.
The alst problem bothering us is:
For what integers p > 0 is
Differentiable? For what p is the derivative continuous?
My work: All I have for the most part is the general derivative of the top equation.
(that is, in the last part, p times x raised to the power of (p-1)
That factors if we pull out the x raised to the power of (p-1) to:
Notice that if we pull out that x from the left side, we have reduced from to .
Help? I think it is whenever p > 2, that it will be continuous because by that, the function would converge to zero as the functions approaches x=0 from the left or right sides.
Would the derivative be continuous for p = anything?