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 $x\in R$ ?
Is the given function continuous and differentiable?
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functions
continuity
1 Answers
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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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0What is the meaning of "If this equation has a repeated root then the function is differentiable also at that point" ? – 2017-02-04
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1you will get an equation when you equate both the branches of the function. – 2017-02-04