`1.`\(f\left(x\right)=7x^2+5x\)
\(f\left(x\right)=7\left(x^2+\dfrac{5}{7}x\right)\)
\(f\left(x\right)=7\left(x^2+\dfrac{5}{7}x+\dfrac{25}{196}-\dfrac{25}{196}\right)\)
\(f\left(x\right)=7\left(x+\dfrac{5}{14}\right)^2-\dfrac{25}{28}\ge-\dfrac{25}{28}\)
Dấu "=" xảy ra `<=>x+5/14=0`
`<=>x=-5/14`
Vậy \(Min_{f\left(x\right)}=-\dfrac{25}{28}\) khi `x=-5/14`
`2.`\(f\left(x\right)=-3x^2+5x\)
\(f\left(x\right)=-3\left(x^2-\dfrac{5}{3}x\right)\)
\(f\left(x\right)=-3\left(x^2-\dfrac{5}{3}x+\dfrac{25}{36}-\dfrac{25}{36}\right)\)
\(f\left(x\right)=-3\left(x-\dfrac{5}{6}\right)^2+\dfrac{25}{12}\le\dfrac{25}{12}\)
Dấu "=" xảy ra `<=>x-5/6=0`
`<=>x=5/6`
Vậy \(Max_{f\left(x\right)}=\dfrac{25}{12}\) khi `x=5/6`
