Question

Tìm GTLN của biểu thức

-x^2+13x+2012

Answer 1

   -x² + 13x + 2012

= -(x² - 13x) + 2012

= -( x² - 2.\(\frac{13}{2}\).x + 169/4 - 169/4) + 2012

= -(x - \(\frac{13}{2}\))²  + 2012 + 169/4

= -(x - \(\frac{13}{2}\))² + 2054\(\frac{1}{4}\)

Vi  -(x - \(\frac{13}{2}\))² <= 0

=> -(x - \(\frac{13}{2}\))² + 2054\(\frac{1}{4}\)<= 2054\(\frac{1}{4}\)

Dau "=" xay ra <=> x - \(\frac{13}{2}\) = 0

                        <=> x           = \(\frac{13}{2}\)

Vay GTLN cua bieu thuc la 2054\(\frac{1}{4}\)khi va chi khi x = \(\frac{13}{2}\)