# Math Help - Applications involving relative extremum:Finding numbers

1. ## Applications involving relative extremum:Finding numbers

Find the number in the interval [-1,1] such that the difference of the number minus its square is
a.) A maximum
b.) a minimum

Find the number in the interval [-1,1] such that the difference of the number minus its square is
a.) A maximum
b.) a minimum

Hello,

to find an extremum (maximum or minimum) you have to examine the borders of the interval and the drivative of the function.

Let x be the number you are looking for.

Then you get the difference by:

$d(x)=x-x^2$

$d'(x)=1-2x$. If d'(x) = 0 then x = 1/2 and the difference is d(1/2) = 1/4. By the 2nd drivative (it is negative) you know that this must be the maxium.

Now examine the borders of the given interval:

d(1) = 0

d(-1) = -2

-2 is smaller than 1/4 so this must be the minimum.

EB