Question 1086873
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Take the derivative and set it equal to each other to find extrema,
{{{df/dx=18x^2-36x-54}}}
{{{18x^2-36x-54=0}}}
{{{x^2-2x-3=0}}}
{{{(x-3)(x+1)=0}}}
Two solutions:
{{{x-3=0}}}
{{{x=3}}}
and
{{{x+1=0}}}
{{{x=-1}}}
Take the second derivative to find which is which,
{{{d2f/dx2=2x-2}}}
At {{{x=-1}}}, {{{2x-2=2(-1)-2=-4}}} so the maximum occurs here.
At {{{x=3}}},{{{2x-2=2(3)-2=4}}} so the minimum occurs here.