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Determine all points x at which f is differentiable.

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Let f(x) = { x|x| if x is rational
0 if x is irrational

determine all points x at which f is differentiable.

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Solution Summary

The points at which a function is differentiable is determined. Rational and irrational functions are differentiated.

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f(x) = x*|x| : if x is rational
and = 0 : if x is irrational

In such problem before going for differentiability, go for continuity.
for x = a (a positive rational number) != 0
Right hand limit (RHL):
Lt (h->0) f(a+h) = 0
( because, a+h can be any irrational ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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