Lösung 2.3:7b
Aus Online Mathematik Brückenkurs 1
We rewrite the expression by completing the square,
Now, we see that the first term \displaystyle -(x-\tfrac{3}{2})^{2} is a quadratic with a minus sign in front, so that term is always less than or equal to zero. This means that the polynomial's largest value is \displaystyle -7/4 and that occurs when \displaystyle x-\tfrac{3}{2}=0\,, i.e. \displaystyle x=\tfrac{3}{2}\,.
