Question

Hi I need help on this question!

Find all points on the graph of the function f(x)=2sinx+sin2x,0≤x<2π at which the tangent line is horizontal. Please list the x-values below separating them with commas.

Answer 1

The tangent line to \(f(x)\) has slope \(f'(x)\) and will be horizontal when the slope is \(f'(x)=0\).
\[f(x)=2\sin x+\sin2x~~\implies~~f'(x)=2\cos x+2\cos2x\]
Set the derivative equal to zero and try solving for \(x\). (Use your identities.)