Question

tìm giá trị lớn nhất 34/4-9/5.x^2

Answer 1

Đặt \(A=\frac{34}{4}-\frac{9}{5}x^2\)

Ta có : 

\(\frac{9}{5}x^2\ge0\forall x\)

\(\Rightarrow\frac{34}{4}-\frac{9}{5}x^2\le\frac{34}{4}\forall x\)

\(\Rightarrow A\le\frac{17}{2}\forall x\)

Dấu \("="\)

\(\Leftrightarrow\frac{9}{5}x^2=0\)

\(\Leftrightarrow x^2=0\)

\(\Leftrightarrow x=0\)

Vậy GTLN của \(A\)là \(\frac{17}{2}\Leftrightarrow x=0\)

Answer 2

\(-\frac{9}{5}.x^2+\frac{34}{4}\le\frac{34}{4}=\frac{17}{2}\forall x\varepsilonℝ\)

dấu "=" xảy ra <=>x=0