Tìm max
E= -3x^2 – x +2
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Lời giải:
$-E=3x^2+x-2=3(x^2+\frac{x}{3})-2$
$=3[x^2+\frac{x}{3}+(\frac{1}{6})^2]-\frac{25}{12}$
$=3(x+\frac{1}{6})^2-\frac{25}{12}\geq \frac{-25}{12}$
$\Rightarrow E\leq \frac{25}{12}$
Vậy $E_{\max}=\frac{25}{12}$. Giá trị này đạt được khi $x+\frac{1}{6}=0\Leftrightarrow x=\frac{-1}{6}$
\(A=-x^2-6x+3\)
\(\Rightarrow A=-\left(x^2+6x\right)+3\)
\(\Rightarrow A=-\left(x^2+6x+9-9\right)+3\)
\(\Rightarrow A=-\left(x^2+6x+9\right)+3+9\)
\(\Rightarrow A=-\left(x+3\right)^2+12\le12\left(-\left(x+3\right)^2\le0,\forall x\right)\)
\(\Rightarrow Max\left(A\right)=12\left(tạix=-3\right)\)
\(D=-2x^2+3x-1\)
\(\Rightarrow D=-2\left(x^2-\dfrac{3}{2}x\right)-1\)
\(\Rightarrow D=-2\left(x^2-\dfrac{3}{2}x+\dfrac{9}{4}-\dfrac{9}{4}\right)-1\)
\(\Rightarrow D=-2\left(x^2-\dfrac{3}{2}x+\dfrac{9}{4}\right)-1+\dfrac{9}{2}\)
\(\Rightarrow D=-2\left(x-\dfrac{3}{2}\right)^2-\dfrac{7}{2}\le-\dfrac{7}{2}\left(-2\left(x-\dfrac{3}{2}\right)^2\le0,\forall x\right)\)
\(\Rightarrow Max\left(D\right)=-\dfrac{7}{2}\left(tạix=\dfrac{3}{2}\right)\)
\(C=-x^2-3x+4\)
\(\Rightarrow C=-\left(x^2+3x\right)+4\)
\(\Rightarrow C=-\left(x^2+3x+\dfrac{9}{4}-\dfrac{9}{4}\right)+4\)
\(\Rightarrow C=-\left(x^2+3x+\dfrac{9}{4}\right)+4+\dfrac{9}{4}\)
\(\Rightarrow C=-\left(x+\dfrac{3}{2}\right)^2+\dfrac{25}{4}\le\dfrac{25}{4}\left(-\left(x+\dfrac{3}{2}\right)^2\le0,\forall x\right)\)
\(\Rightarrow Max\left(C\right)=\dfrac{25}{4}\left(tạix=-\dfrac{3}{2}\right)\)
E = - 3\(x^2\) - \(x\) + 2
E = - 3.( \(x^2\) + 2.\(\dfrac{1}{6}\)\(x\) + \(\dfrac{1}{36}\)) + 2
E = -3.(\(x\) + \(\dfrac{1}{6}\))2 + \(\dfrac{25}{12}\)
Vì (\(x+\dfrac{1}{6}\))2 ≥ 0 ∀ \(x\) ⇒ -3.(\(x+\dfrac{1}{6}\))2 ≤ 0 ⇒ -3(\(x+\dfrac{1}{6}\))2 + \(\dfrac{25}{12}\) ≤ \(\dfrac{25}{12}\)
Emax = \(\dfrac{25}{12}\) ⇔ \(x\) = - \(\dfrac{1}{6}\)