a/ \(A=5x-x^2=-\left(x^2-5x+\dfrac{25}{4}\right)+\dfrac{25}{4}=-\left(x-\dfrac{5}{2}\right)^2+\dfrac{25}{4}\)
vì: \(\left(x-\dfrac{5}{2}\right)^2\ge0\Rightarrow-\left(x-\dfrac{5}{2}\right)^2\le0\)
=> \(-\left(x-\dfrac{5}{2}\right)^2+\dfrac{25}{4}\ge\dfrac{25}{4}\)
''='' xảy ra khi x= 5/2
Vậy MaxA = \(\dfrac{25}{4}\Leftrightarrow x=\dfrac{5}{2}\)
b/ \(B=x-x^2=-\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{1}{4}=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\le\dfrac{1}{4}\)
dấu ''='' xảy ra khi \(x=\dfrac{1}{2}\)
vậy \(max_A=\dfrac{1}{4}\Leftrightarrow x=\dfrac{1}{2}\)
c/ \(C=4x-x^2+3=-\left(x^2-4x+4\right)+7=-\left(x-2\right)^2+7\)
vì: \(-\left(x-2\right)^2\le0\Rightarrow-\left(x-2\right)^2+7\le7\)
''='' xảy ra khi x = 2
vậy maxA = 7 khi x = 2