`C=-2x(x+7)=-2x^2-14x`
`=-(2x^2+14x)`
`=-( (\sqrt2x)^2 + 2.\sqrt2 x . (7\sqrt2)/2 + ((7\sqrt2)/2)^2 )+49/2`
`=-(\sqrt2x+(7\sqrt2)/2)^2+49/2`
`=> C_(max) = 49/2 <=> x=-7/2`
`D=-3x^2+5x-9`
`=-(3x^2-5x+9)`
`=-((\sqrt3x)^2 - 2.\sqrt3x . (5\sqrt3)/6 + ((5\sqrt3)/6)^2)-83/12`
`=-(\sqrt3x-(5\sqrt3)/6)^2-83/12`
`=> D_(max)=-83/12 <=> \sqrt3x - (5\sqrt3)/6=0 <=> x=5/6`
a) Ta có: \(C=-2x\left(x+7\right)\)
\(=-2\left(x^2+7x\right)\)
\(=-2\left(x^2+7x+\dfrac{49}{4}-\dfrac{49}{4}\right)\)
\(=-2\left(x+\dfrac{7}{2}\right)^2+\dfrac{49}{2}\le\dfrac{49}{2}\forall x\)
Dấu '=' xảy ra khi \(x=-\dfrac{7}{2}\)
b) Ta có: \(D=-3x^2+5x-9\)
\(=-3\left(x^2-\dfrac{5}{3}x+3\right)\)
\(=-3\left(x^2-2\cdot x\cdot\dfrac{5}{6}+\dfrac{25}{36}+\dfrac{83}{36}\right)\)
\(=-3\cdot\left(x-\dfrac{5}{6}\right)^2-\dfrac{83}{12}\le-\dfrac{83}{12}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{5}{6}\)
