Find the point on the curve `y=cosx-1,x in [pi/2,(3pi)/2]` at which the tangent in parallel to the x-axis.

Answer

Points are `(pi , -2)`

Explanation

\begin{aligned}
&y=\cos x-1 \quad, \quad x \in\left[\frac{\pi}{2}, \frac{3 \pi}{2}\right]\\ \\
&\text{Also } \frac{d y}{d x}=-\sin x\\
&\text{So } \frac{d y}{d x}=0 \Rightarrow-\sin x=0\\
&\Rightarrow \sin x=0\\
&x=\pi\\ \\
&y=\cos \pi-1=(-1)-1\\
&y= -2 \\
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