Answer :
[tex]f(x)=x(1-x)\\\\zeros:x=0\ and\ x=1\\\\vertex\ (x_v;\ y_v):\\\\x_v=\frac{0+1}{2}=\frac{1}{2}\\\\y_v=\frac{1}{2}(1-\frac{1}{2})=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}[/tex]
[tex]a)\\\frac{f(0)-f(1)}{0-1}=0\\\\b)\\ROC_{inst}(\frac{1}{2})=0\\\\c)\\(0;\ \frac{1}{2})[/tex]
[tex]a)\\\frac{f(0)-f(1)}{0-1}=0\\\\b)\\ROC_{inst}(\frac{1}{2})=0\\\\c)\\(0;\ \frac{1}{2})[/tex]