I used a graph plotter and ploted the graph of x! and noticed a critical point at x=0.5 (I plotted graph for real no.) . What can be the reason for this depression in interval (0,1) ?

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{The} \mathrm{graph} \mathrm{you} \mathrm{have} \mathrm{plotted} \mathrm{is} \mathrm{not} \mathrm{of} \mathrm{factorial} \mathrm{function}. \\ \mathrm{It} \mathrm{is} \mathrm{the} \mathrm{graph} \mathrm{of} \mathrm{gamma} \mathrm{function} \mathrm{which} \mathrm{is} \mathrm{an} \mathrm{extension} \mathrm{of} \mathrm{the} \mathrm{factorial} \\ \mathrm{function}. \\ \mathrm{Unlike} \mathrm{factorial}, \mathrm{gamma} \mathrm{function} \mathrm{is} \mathrm{defined} \mathrm{for} \mathrm{all} \mathrm{positive} \mathrm{real} \mathrm{numbers}. \end{gathered}$$

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