(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose a>0 is some constant and f:R->R is given by

f(x) = |x|^a x sin(1/x) if x is not 0

f(x) = 0 if x=0

for which values of a is f differentiable at x=0? Use calculus to determine f'(x) for x is not equal to 0. For what values of a is f' a continuous function defined on R? Justify your answer

2. Relevant equations

3. The attempt at a solution

when f is not 0, f'(x) = a|x|^(a-1) x sin (1/x) - a.|x|^(a-2) x cos (1/x)

so f' is continuous for a>2 where a is a natural number??

what about when x=0?

for what values of a is f differentiable? is it all a in the real numbers?Dif

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# Differentiability + Continuity?

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