Given an CFG determine if $\varepsilon \in L(G)$ Given a context free grammar how am I able to determine if $\varepsilon \in L(G)$ ? 

The only way I thought of is to systematically check if I can derive the empty word from the given grammar. (Assuming it's not in CNF)

Is my intuition right though?
You can transform the CFG to Greibach normal form, and then simply check whether the rule $S\rightarrow \varepsilon$ exists. 

In fact, you are asking whether there is a parsing algorithm for CFG.