Question

let f(x)=(sinx)^2-(cosx) on the interval (0,2pi). where on this interval does f increase and where does it decrease? I tried deriving it, but I can't seem to get it right.

Answer 1

\[f'(x)=2\sin(x)\cos(x)+\sin(x)\]

Answer 2

\[2\sin(x)\cos(x)+\sin(x)=0\]
\[\sin(x)(2\cos(x)+1)=0\]
\[\sin(x)=0, x=0,x=\pi\]
\[2\cos(x)+1=0\implies \cos(x)=-\frac{1}{2}\implies x=\frac{2\pi}{3}, x=\frac{4\pi}{3}\] etc