Question 1181193
<pre>
Let x be the number in the interval [-2, 2] so that the difference of the
number from its square is maximized. 

the difference of the number x from its square x<sup>2</sup> is x<sup>2</sup> - x.

Let y equal to this difference x<sup>2</sup> - x.
 
{{{y}}}{{{""=""}}}{{{x^2-x}}}

The graph of the equation looks like this

{{{graph(400,400,-3,3,-3,3,x^2-x)}}}

The value of y (the difference) is minimized at the bottom of
that graph (at the bottom point), which is the vertex.

The formula for the x-coordinate of the vertex of {{{y=ax^2+bx+c}}} is 

     {{{-b/(2*a)}}}

{{{y=x^2-x}}} can be thought of as {{{y=1a^2-1x+0}}} so a=1, b=-1, c=0

     {{{-b/(2a)}}}
     {{{-(-1)/(2(1))}}}
     {{{1/2}}}

So 1/2 is the number in the interval [-2, 2] so that the difference of the
number from its square is maximized. 

Edwin</pre>