Find points where f(x) = 4sinx + 2x has a horizontal tangent

[brian ravenell]

Find points where f(x)= 4sinX+2x has a horizontal tangent 10<=x<=2(pi)

 

[soroban]

Re: help me

Hello, Brian!

Find points where \(\displaystyle f(x)\:=\:4\sin x\,+\,2x\) has a horizontal tangent, \(\displaystyle 0\,\leq\,x\,\leq\, 2\pi\)

Horizontal tangents occur where \(\displaystyle f'(x)\,=\,0\)

We have: \(\displaystyle \:4\cos x\,+\,2\:=\:0\;\;\Rightarrow\;\;\cos x\,=\,-\frac{1}{2}\)

Therefore: \(\displaystyle \:x\:=\:\frac{2\pi}{3},\:\frac{4\pi}{3}\)