Question

Tìm giá trị lớn nhất (hoặc nhỏ nhất) của các biểu thức sau :

B = \(2x^2 + 10x - 1\)

C = \(5x - x^2\)

HELP

Answer 1

a, Ta có: \(B=2x^2+10x-1=2x^2+10x+\dfrac{25}{2}-\dfrac{27}{2}\)

\(=2\left(x^2+2.x.\dfrac{5}{2}+\dfrac{25}{4}\right)-\dfrac{27}{2}\)

\(=2\left(x+\dfrac{5}{2}\right)^2-\dfrac{27}{2}\ge\dfrac{-27}{2}\)

Dấu " = " khi \(2\left(x+\dfrac{5}{2}\right)^2=0\Leftrightarrow x=\dfrac{-5}{2}\)

Vậy \(MIN_B=\dfrac{-27}{2}\) khi \(x=\dfrac{-5}{2}\)

b, Ta có: \(C=5x-x^2=-\left(x^2-2.x.\dfrac{5}{2}+\dfrac{25}{4}-\dfrac{25}{4}\right)\)

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

Dấu " = " khi \(-\left(x-\dfrac{5}{2}\right)^2=0\Leftrightarrow x=\dfrac{5}{2}\)

Vậy \(MAX_C=\dfrac{25}{4}\) khi \(x=\dfrac{5}{2}\)