- #1

Lorek

- 8

- 0

## Homework Statement

Find the positive number that exceeds its square by the largest amount. Obviously this is on the open interval (0,1).

## Homework Equations

## The Attempt at a Solution

[tex] F(x) = ( \frac{1}{n} ) ^2 - n \Rightarrow F'(x) = \frac{-2}{n^3} - 1 = 0

\Rightarrow 1 = \frac{-2}{n^3} \Rightarrow n^3 = -2 [/tex]

This is where I'm stuck. Taking the Cubic Root of a Negative number only nets

me a complex number. The answer at the back says its 1/2.