The function f(x)=2x324x2+42x+11\displaystyle {f{{\left({x}\right)}}}={2}{x}^{{3}}-{24}{x}^{{2}}+{42}{x}+{11} has derivative f(x)=6x248x+42\displaystyle {f}'{\left({x}\right)}={6}{x}^{{2}}-{48}{x}+{42}.

f(x) has one local minimum and one local maximum.

f(x) has a local minimum at x\displaystyle {x} equals  

with value  


and a local maximum at x\displaystyle {x} equals  

with value