Question 1006079
Question asks the maximum value between  {{{-3<x<0}}}.  Find where the vertex is in relation to this interval.  A possible way is change the expression into standard form and read the x coordinate of the vertex; and note that the vertex is a minimum point for the quadratic function.  You are expecting the MAXIMUM value to be at either x=-3 or x=0, because one of them is likely to be greater than the y-value of the vertex.



{{{3x^2 + 7x - 2}}}
{{{3(x^2+(7/3)x )-2}}}
{{{3(x^2+(7/3)x+(7/6)^2)-3(7/6)-2}}}
{{{3(x+7/6)^2-7/2-4/2}}}
{{{3(x+7/6)^2-9/2}}}


The vertex, a minimum value for the function, occurs at {{{x=-7/6}}}.


Did you really mean  the interval INCLUSIVE, like {{{-3<=x<=0}}}?  If yes, then there are TWO maximum values on this interval, not just one value.  Otherwise the answer can only be a limit.


{{{-7/6=-1&1/6}}}


{{{graph(300,300,-4,4,-6,2,3x^2+7x-2)}}}


The limits for the max value on the interval both are at y=0.