Differentiate complex function? $$f(z)=3z^2+\bar{z}$$

I want to show the function is either differentiable or not so I can state if it is holomorphic or not. What is the method for this ?

Edit - Can some give an example of how to apply cauchy riemann equation to this question ?
If $f(z)$ were differentiable, then $f(z)-3z^2=\bar{z}$ would be differentiable since $3z^2$ is. However, $\bar{z}$ is not complex differentiable. Check this with the Cauchy-Riemann equations.
This function is differentiable everywhere except at z=0.  As with real differentiation, complex differentiation is still a linear operation, meaning that d/dz( $3z^2 + \bar{z}$) = d/dz ($3z^2$) + d/dz ($\bar{z}$).  The first term is differentiable everywhere.  The second term is not differentiable at zero because $\bar{z}'(0) = \lim_{z-&gt;0} (\bar{z}-0)/(z-0)$, and $\bar{z}/z$ can take on different values as $z-&gt;0$ for different directions (e.g. if you approach z from the positive real axis, $\bar{z}/z -&gt; 1$; if you approach from the positive imaginary axis, $\bar{z}/z-&gt;-1$.  Here is a good page detailing this: http://en.wikipedia.org/wiki/Holomorphic_function