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The function $f:R\rightarrow R$ is defined as:

$f(x) = \begin{cases} & \text{ $3x^{2}$ } ; x\in Q \\ & \text{ $-5x^{2}$ } ; x \notin Q \end{cases}$


How to check its continuity and differentiability at $x\in Q$ and $x\in R$ ?

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The function is continuous at all those points where $3x^2 =-5x^2$.

If this equation has a repeated root then the function is differentiable also at that point.

In your case the function is differentiable at $0$ only

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  • $\begingroup$ What is the meaning of "If this equation has a repeated root then the function is differentiable also at that point" ? $\endgroup$ Feb 4 '17 at 5:06
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    $\begingroup$ you will get an equation when you equate both the branches of the function. $\endgroup$
    – Upstart
    Feb 4 '17 at 5:36

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