Question

Find the maximum value of the function

Answer 1

$\bf \stackrel{f(x)}{y}=1-x-x^2\implies y=-x^2-x+1 \\\\\\ \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} y = &{{ -1}}x^2&{{ -1}}x&{{ +1}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad \stackrel{maximum}{1-\cfrac{(-1)^2}{4(-1)}}\right)$

Answer 2

The maximum value of the function is 5/4.