Of the infinitely many lines that are tangent to the curve
y = −8 sin x
and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.

Question

Of the infinitely many lines that are tangent to the curve 
y = −8 sin x
 and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.

anonymous · Answer

write an equation for the slope of the tangent going though the origin and maximize that.

anonymous · Answer

$$m=\frac{ (-8\sin x - 0) }{ (x - 0) }=-8 \cos x \Rightarrow 8(\sin x - x \cos x) = m \Rightarrow \frac{ dm }{ dx } = ?$$