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(C) Let the number be $x$. We want to maximize the function $f(x) = x - x^2$.To find the maximum,we take the first derivative with respect to $x$:$f'(

Vedclass · Accepted Answer

$1$/$2$

Vedclass · Answer

(C) Let the number be $x$. We want to maximize the function $f(x) = x - x^2$.To find the maximum,we take the first derivative with respect to $x$:$f'(x) = 1 - 2x$.Setting the first derivative to zero for critical points:$1 - 2x = 0 \Rightarrow x = \frac{1}{2}$.To verify this is a maximum,we take the second derivative:$f''(x) = -2$.Since $f''(x) Thus,the number that exceeds its square by the greatest amount is $\frac{1}{2}$.

The number that exceeds its square by the greatest amount is

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