Question 1181193
.
Find the number in the interval [  -  2, 2 ] so that the difference of the
number from its square is maximized.
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            The solution given by  Edwin in his post is  ONLY  PART  of the FULL  solution,  and being the part, only, 

            IT  DOES  NOT  GIVE  the full solution.


            His solution for the local minimum/maximum should be supplemented by the end-behavior analysis 

            of the function  f(x) = x^2 - x.



<pre>
This end-behavior analysis gives the values


    (a)  at x = -2,  f(-2) = (-2)^2 - (-2) = 4 + 2 = 6;


    (a)  at x =  2,  f(2)  =   2^2  -   2  = 4 - 2 = 2.


So, the answer is:  in the interval [-2,2],  the number which provides the maximum of the function f(x) = x^2 - x, is the value of x= -2.
</pre>


As you see, &nbsp;the correct answer is totally different from that by &nbsp;Edwin.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For better understanding, &nbsp;see the plot below.



<pre>
              {{{graph( 400, 400, -3, 3, -3, 7,        
              x^2, x, x^2 - x, 200(x+2), 200(x-2)
)}}}


     Plot y = {{{x^2}}} (red),  y = x (green)  and  the difference y = {{{x^2 - x}}} (blue)
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