I've looked for a similar question on here but couldn't find any. I have found a similar question on Google but it still didn't help me.
My question is
Find the points on the curve y = cos(x)/(2+sin(x)) at which the tangent is horizontal.
I know that it's horizontal when f'(x) = 0 but I can't seem to work out the x values.
My f'(x) I worked out to be (-sin(x)))/(2) - (cos(x)cos(x))/((2+sin(x))^2)
How can I find the x values when I sub x = 0, I cant equate it to 0
Let $$ f(x)=\frac{\cos x}{2+\sin x}. $$ Then, $$ f^{\prime}(x)=-\frac{2\sin x+1}{\left(\sin x+2\right)^{2}}. $$ Note that $f^{\prime}(x)=0$ if and only if $$ 2\sin x+1=0. $$ Can you finish?