Question

tìm giá trị lớn nhất

A bằng -x^2 cộng 4x cộng 7

B bằng -4x^2 cộng 4x - 5

C bằng -x^2 cộng x cộng 5

Answer 1

\(A=-x^2+4x+7=-\left(x^2-4x+4\right)+11=-\left(x-2\right)^2+11\)

Ta thấy : \(-\left(x-2\right)^2+11\le11\)\(\Leftrightarrow maxA=11\)khi    \(x=2\)

\(B=-4x^2+4x-5=-\left(4x^2-4x+1\right)-4=-\left(2x-1\right)^2-4\)

Ta thấy : \(-\left(2x-1\right)^2-4\le-4\)\(\Leftrightarrow maxB=-4\)khi   \(x=\frac{1}{2}\)

\(C=-x^2+x+5=-\left(x^2-2\cdot\frac{1}{2}\cdot x+\frac{1}{4}\right)+\frac{21}{4}=-\left(x-\frac{1}{2}\right)^2+\frac{21}{4}\)

Ta thấy : \(-\left(x-\frac{1}{2}\right)^2+\frac{21}{4}\le\frac{21}{4}\)\(\Leftrightarrow maxC=\frac{21}{4}\)khi    \(x=\frac{1}{2}\)

tk mk nka !!! 

Answer 2

thanks