For the function f(x)=5x+7x\displaystyle {f{{\left({x}\right)}}}={5}{x}+\frac{{7}}{{x}}, find the critical numbers and use the First Derivative Test to find the local maximum and minimum values and where they occur. Enter exact answers.

This function has a local maximum at x=\displaystyle {x}=  
with value y=\displaystyle {y}=  

and a local minimum at x=\displaystyle {x}=  
with value y=\displaystyle {y}=