Question

Tìm x để f(x) đạt GTLN là tính GTLN đó:
1, f(x)=-4x²+12x+3
2, f(x)=-x²+5x-2
3, f(x)=-3x²+7x

Answer 1

a)\(f\left(x\right)=-4x^2+12x+3\)

\(=-4x^2+12x-9+12\)

\(=-\left(4x^2-12x+9\right)+12\)

\(=-\left(2x-3\right)^2+12\le12\)

Xảy ra khi \(x=\dfrac{3}{2}\)

b)\(f\left(x\right)=-x^2+5x-2\)

\(=-x^2+5x-\dfrac{25}{4}+\dfrac{17}{4}\)

\(=-\left(x^2-5x+\dfrac{25}{4}\right)+\dfrac{17}{4}\)

\(=-\left(x-\dfrac{5}{2}\right)^2+\dfrac{17}{4}\le\dfrac{17}{4}\)

Xảy ra khi \(x=\dfrac{5}{2}\)

c)\(f\left(x\right)=-3x^2+7x\)

\(=-3x^2+7x^2-\dfrac{49}{12}+\dfrac{49}{12}\)

\(=-3\left(x^2-\dfrac{7x}{3}+\dfrac{49}{36}\right)+\dfrac{49}{12}\)

\(=-3\left(x-\dfrac{7}{6}\right)^2+\dfrac{49}{12}\le\dfrac{49}{12}\)

Xảy ra khi \(x=\dfrac{7}{6}\)