Question 1069395
Graphing,
.
.
.
*[illustration fre3.JPG].
.
.
.
Using calculus,
{{{y=18x^(1/3)-6x}}}
{{{dy/dx=6/x^(2/3)-6}}}
Setting the derivative to zero,
{{{6/x^(2/3)-6=0}}}
{{{6/x^(2/3)=6}}}
{{{x^(2/3)=1}}}
{{{x=1}}}
Since the second derivative is negative, when {{{x=1}}}, this value is a maximum.
Find the minimum value by checking the endpoints.
{{{f(-1)=-18+6=-12}}}
{{{f(8)=36-48=-12}}}