Answer
maximum: $(-\frac{1}{2},\frac{5}{4})$
no minimas
Work Step by Step
We are given:
$f(x)=1-x-x^{2}$
We factor by completing the square:
$1-x-x^{2}$
$-x^2-x+1$
$-(x^{2}+x)+1$
$-(x^{2}+x+\displaystyle \frac{1}{4})+1+\frac{1}{4}$
$-(x+\frac{1}{2})^{2}+\frac{5}{4}$
We see that this is a transformed parabola: $x^2$ reflected around the x-axis, moved left $\frac{1}{2}$ units and up $\frac{5}{4}$ units. Thus the maximum would occur at $(-\frac{1}{2},\frac{5}{4})$.
