## 01 - 04 Number Problems in Maxima and Minima

**Problem 1**

What number exceeds its square by the maximum amount?

**Solution 1**

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Let

x = the number and

x

y = the difference between x and x

x = the number and

x

^{2}= the square of the numbery = the difference between x and x

^{2}$y = x - x^2$

$y' = 1 - 2x = 0$

$x = \frac{1}{2}$ *answer*

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