1/
Đặt \(f\left(x\right)=sin^4x+\left(sinx+2\right)^4\)
\(\Rightarrow f'\left(x\right)=4sin^3x.cosx+4\left(sinx+2\right)^3.cosx\)
\(f'\left(x\right)=0\Leftrightarrow4cosx\left[sin^3x+\left(sinx+2\right)^3\right]=0\)
\(\Leftrightarrow4cosx\left(2sinx+2\right)\left(sin^2x-sinx\left(sinx+2\right)+\left(sinx+2\right)^2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\sinx=-1\end{matrix}\right.\)
\(\Rightarrow f\left(x\right)_{min}=2\); \(f\left(x\right)_{max}=82\Rightarrow2\le m\le82\)
Câu 2:
\(sinx\left(sinx+6\right)\left(sinx+2\right)\left(sinx+4\right)=m\)
\(\Leftrightarrow\left(sin^2x+6sinx\right)\left(sin^2x+6sinx+8\right)=m\)
Đặt \(a=sin^2x+6sinx\) (\(-5\le a\le7\)) pt trở thành:
\(f\left(a\right)=a^2+8a=m\)
Xét \(f\left(a\right)\) trên \(\left[-5;7\right]\) có: \(\left\{{}\begin{matrix}f\left(-5\right)=-15\\f\left(-4\right)=-16\\f\left(7\right)=105\end{matrix}\right.\)
\(\Rightarrow-15\le f\left(a\right)\le105\Rightarrow-15\le m\le105\)
