Question

Tìm GTLN của: M=x+\(\sqrt{4-x}\)

Answer 1

ĐKXĐ: \(x\le4\)

\(M=-\left(4-x-\sqrt[]{4-x}+\dfrac{1}{4}\right)+\dfrac{1}{4}=-\left(\sqrt[]{4-x}-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\le\dfrac{1}{4}\)

\(M_{max}=\dfrac{1}{4}\) khi \(\sqrt[]{4-x}=\dfrac{1}{2}\Rightarrow x=\dfrac{15}{4}\)