Voi gia tri ao cua bieb so bieu thuc co gia tri lon nhat ? Tim gia tri lon nhat do
P=10-x mu2-x mu 4
Voi gia tri ao cua bieb so bieu thuc co gia tri lon nhat ? Tim gia tri lon nhat do P=10-x mu2-x mu 4
By Liliana
By Liliana
Voi gia tri ao cua bieb so bieu thuc co gia tri lon nhat ? Tim gia tri lon nhat do
P=10-x mu2-x mu 4
P=10-$x^{2}$ – $x^{4}$
Ta có
$x^{2}$≥0 với mọi x
$x^{4}$≥0 với mọi x
⇒$x^{2}$-$x^{4}$≥0 với mọi x
⇒10-$x^{2}$-$x^{4}$≥10
P đạt GTLN ⇔$x^{2}$-$x^{4}$=0
x(x-$x^{3}$)=0
⇒\(\left[ \begin{array}{l}x=0\\x-x^{3}=0\end{array} \right.\)
⇒\(\left[ \begin{array}{}x=0\\x(1-x^{2})=0\end{array} \right.\)
⇒\(\left[ \begin{array}{l}x=0\\1-x^{2}=0\end{array} \right.\)
⇒\(\left[ \begin{array}{l}x=0\\x^{2}=1\end{array} \right.\)
⇒\(\left[ \begin{array}{l}x=0\\x=±1\end{array} \right.\)
P đạt GTLN ⇔x ∈{-1;0;1)