Question

Help me!!!

Answer 1

[(x^2 - 12x + 36) - (x^2 + 9)] / (x^2 + 9) = [(x - 6)^2]/(x^2 + 9) - 1 >= -1
GTNN là -1 khi x = 6

Answer 2

\(A=\dfrac{27-12x}{x^2+9}=\dfrac{\left(x^2-12x+36\right)-\left(x^2+9\right)}{x^2+9}\)

\(A=\dfrac{\left(x-6\right)^2}{x^2+9}-1\)

Ta có: \(\left(x-6\right)^2\ge0;x^2+9>0\)\(\Rightarrow\dfrac{\left(x-6\right)^2}{x^2+9}\ge0\)

\(\Rightarrow\)\(\dfrac{\left(x-6\right)^2}{x+9}-1\ge-1\)

Vậy: Min_A=-1 khi \(\left(x-6\right)^2=0\Leftrightarrow x-6=0\Leftrightarrow x=6\)

Chơi luôn đạo hàm á chị ( vì chị > lp 8) Rain..