Question

Giúp em vs ạ

Answer 1

a.

\(y=\left(tanx+2\right)^2-5\ge-5\)

\(y_{min}=-5\) khi \(tanx=-2\)

\(y_{max}\) không tồn tại

b.

\(y=1-cos^2x+cosx+5=-cos^2x+cosx+6\)

\(y=-\left(cosx-\dfrac{1}{2}\right)^2+\dfrac{25}{4}\le\dfrac{25}{4}\)

\(y_{max}=\dfrac{25}{4}\) khi \(cosx=\dfrac{1}{2}\)

\(y=-cos^2x+cosx+2+4=\left(cosx+1\right)\left(2-cosx\right)+4\)

Do \(-1\le cosx\le1\Rightarrow\left(cosx+1\right)\left(2-cosx\right)\ge0\)

\(\Rightarrow y\ge4\)

\(y_{min}=4\) khi \(cosx=-1\)