Question

Determine o ponto máximo da função f(x) = - x² + 3x - 2 .

Answer 1

$\Large\boxed{\begin{array}{l}\sf f(x)=-x^2+3x-2\\\sf a=-1<0\implies tem~ponto~de~m\acute aximo\\\sf\Delta=b^2-4ac\\\sf\Delta=3^2-4\cdot(-1)\cdot(-2)\\\sf\Delta=9-8\\\sf\Delta=1\\\sf x_V=-\dfrac{b}{2a}=-\dfrac{3}{2\cdot(-1)}=\dfrac{3}{2}\\\\\sf y_V=-\dfrac{\Delta}{4a}=-\dfrac{1}{4\cdot(-1)}=\dfrac{1}{4}\\\sf V\bigg(\dfrac{3}{2},\dfrac{1}{4}\bigg)\end{array}}$