Найдите максимальное значение функции log1/2(х^2-6х + 17).

[latex]y=log_\frac{1}{2}(x^2-6x+17), \\ x^2-6x+17\ \textgreater \ 0, \\ D=-32\ \textless \ 0, \ a=1\ \textgreater \ 0, \\ x\in R; \\ y'=\frac{2x-6}{(x^2-6x+17)\ln\frac{1}{2}}, \\ y'=0, \ 2x-6=0, \ x=3, \\ \frac{1}{2}\ \textless \ 1, \ \ln\frac{1}{2}\ \textless \ 0, \\ x\ \textless \ 3, \ y'\ \textgreater \ 0, \ y\nearrow, \\ x\ \textgreater \ 3, \ y'\ \textless \ 0, \ y\searrow, \\ x_{max}=3, \ y_{max}=log_\frac{1}{2}(3^2-6\cdot3+17)=log_\frac{1}{2}8=-3. \\ (3;-3).[/latex]