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natita [175]
3 years ago
11

At what point on the curve y=x+2cos x is the tangent horizontal in the interval [-2pi, 2pi]

Mathematics
1 answer:
k0ka [10]3 years ago
8 0
\bf y=x+2cos(x)\qquad \qquad [-2\pi ,2\pi ]\\\\
-----------------------------\\\\
\cfrac{dy}{dx}=1-2sin(x)\implies 0=1-2sin(x)\implies sin(x)=\cfrac{1}{2}
\\\\\\
\measuredangle x=sin^{-1}\left( \frac{1}{2} \right)\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}\\\\
\frac{5\pi }{6}
\end{cases}

only in the 1st and 2nd quadrants, where sine is positive
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