(Solved): Find the \( x \)-coordinates of the points on the curve \( x y=x^{3}+7 x^{2}+4 x+2 \) where the tan ...

Find the \( x \)-coordinates of the points on the curve \( x y=x^{3}+7 x^{2}+4 x+2 \) where the tangent line is horizontal. \[ x= \] Find \( d y / d x \) by implicit differentiation. \[ \arcsin (x y)=\frac{2}{3} \arctan (8 x), \quad\left(\frac{1}{8}, 4\right) \] \[ \frac{d y}{d x}= \] Find the slope of the graph at the given point. \[ \frac{d y}{d x}= \] \[ \theta(x)=\tan ^{-1}\left(\frac{x}{50}\right) \] How fost is the light beam moving along the wall when the beam makes an angle of \( \theta=45^{\circ} \) with the line perpendicular from the light to the wall? \( d x / d t= \) \( X \mathrm{ft} / \mathrm{min} \)