Question 696129
 a local {{{minimum}}} is:

{{{f(x) = 0}}} for all {{{x}}} in the interval [{{{-2}}},{{{3}}}]

{{{((x^2)+x)^(2/3)=0}}}

{{{root(3,(x^2+x)^2)=0}}}....it will be equal to zero if

{{{(x^2+x)^2=0}}}....it will be equal to zero if

{{{x^2+x=0}}}

{{{x(x+1)=0}}}....it will be equal to zero if

{{{x=0}}}

or

{{{x+1=0}}}....=>..{{{x=-1}}}

both solutions, {{{x=0}}} and {{{x=-1}}} lie in given  interval: {{{-2<0<3}}}, and {{{-2<-1<3}}}

so, a local {{{minimum}}} is at:({{{0}}},{{{0}}}) and ({{{0}}},{{{0}}})

 {{{ graph( 600,600, -5, 5, -5, 5, ((x^2)+x)^(2/3)) }}}

as you can see from a graph, there is {{{no}}} local{{{ maximum}}}