Processing Math: Done

From Förberedande kurs i matematik 1

We rewrite the expression by completing the square,

−x2+3x−4=−x2−3x+4=−x−232−232+4=−x−232−49+416=−x−232+47=−x−232−47.

Now, we see that the first term −(x−23)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 −74 and that occurs when x−23=0, i.e. x=23.