Finding simple bifurcation point

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$\dot{x}=x-rx\left ( 1-x \right )$

I know where the fixed point occurs but what about the bifurcation points. I thought I knew how to find the bifurcation points. At least, for simple ODE where I can sketch via hand. But beyond that, what is the technique to finding the bifurcation points $r_{c}$?

Thanks in advance