Question

Tìm GTLN,GTNN của hàm số:

a, \(y=3cosx-1\)

b, \(y=5+2sinx\)

c,\(y=\sqrt{3+cos2x}\)

d,\(y=\sqrt{5sinx-1}+2\)

Answer 1

a.\(-1\le cosx\le1\Rightarrow-4\le y=3cosx-1\le2\)

b.-1 \(\le sinx\le1\)\(\Rightarrow3\le y=5+2sinx\le7\)  

c.\(\sqrt{3-1}\le\sqrt{3+cos2x}\le\sqrt{3+1}\Rightarrow\sqrt{2}\le y\le2\)

d.\(y=\sqrt{5sinx-1}+2\le\sqrt{5.1-1}+2=4\)

\(y=\sqrt{5sinx-1}+2\ge2\) . " = " \(\Leftrightarrow sinx=\dfrac{1}{5}\Leftrightarrow\left[{}\begin{matrix}x=arcsin\left(\dfrac{1}{5}\right)+2k\pi\\x=\pi-arcsin\left(\dfrac{1}{5}\right)+2k\pi\end{matrix}\right.\)  ( k thuộc Z )