The function f(x)=2x327x2+84x+1\displaystyle {f{{\left({x}\right)}}}={2}{x}^{{3}}-{27}{x}^{{2}}+{84}{x}+{1} has one local minimum and one local maximum. Graph the function with a graphing calculator or Desmos. Use the graph to estimate these local extrema.

This function has a local minimum at x\displaystyle {x} =   with output value  

and a local maximum at x\displaystyle {x} =   with output value