# 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 Preview

because,

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 Summary

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

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